"

Quadratic Functions

Prep for Graphing Quadratic Functions

  1. [latex]\begin{array}{lc}B&\left(0,1\right)\\F&1\\C\;or\;D\;\;&x=1\\C\;or\;D&x=1\\A&\left(1,0\right)\\E&y=1\end{array}[/latex]
  1. [latex]y=3[/latex]
  2. [latex]x=3[/latex]
  3. [latex](-3,0)[/latex]
  1. Explain
  2. [latex]-4[/latex]
  3. [latex]-\frac32[/latex]
  4. [latex]4[/latex]
    1. [latex]-\frac56[/latex]
    2. [latex]\frac12[/latex]
    3. [latex]-10[/latex]
    1. [latex]57[/latex]
    2. [latex]5[/latex]
    3. [latex]\frac{19}2[/latex]
    1. [latex]-26[/latex]
    2. [latex]-2[/latex]
    3. [latex]4[/latex]
    1. [latex]-13[/latex]
    2. [latex]-\frac{89}{16}[/latex]
    3. [latex]-\frac{41}4[/latex]
  1. An intercept is a point where a graph touches the x- or y-axis.
    1. y-intercept: (0, 2); x-intercept: (-5, 0)
    2. y-intercept: (0, -2); x-intercepts: (-2, 0), (1, 0)
    1. Yes
    2. No
  1. Infinity and negative infinity; Discuss with classmates.
  1. A Cartesian coordinate plane with a grid labeled from -10 to 10 on both axes. Two intersecting V-shaped lines form a diamond-like figure symmetric about both the x-axis and y-axis. The top vertex is at (0, 5), the bottom vertex is at (0, -5), the left vertex is at (-10, 0), and the right vertex is at (10, 0). Additional points are plotted along each line segment to show the shape’s linear sides.
  2. A Cartesian coordinate plane with a grid labeled from -4 to 4 on both axes. A regular hexagon is centered near the origin, with vertices at approximately (-2, 2), (2, 2), (-2.5, 0), (2, -2), (-2, -2), and (2.5, 0). The hexagon is symmetric about both the x-axis and y-axis.

Classwork: Graphing Quadratic Functions

A Cartesian coordinate plane displaying an upward-opening parabola. The parabola is symmetric about the vertical y-axis, labeled as the “axis of symmetry.” The vertex, also labeled as the “vertex / y-intercept minimum,” is located below the x-axis. Two labeled arrows point to the parabola’s x-intercepts, where the curve crosses the x-axis.

A Cartesian coordinate plane displaying a downward-opening parabola. The parabola’s highest point is labeled “vertex / maximum.” A vertical dashed line through the vertex is labeled “axis of symmetry.” Two arrows point to the points where the parabola crosses the x-axis, labeled as “x-intercepts.”

  1. 2
  2. none
  3. 1

Graph A

  1. [latex]x=3[/latex]
  2. [latex](3,4)[/latex]
  3. maximum
  4. Domain [latex]=\left(-\infty,\infty\right);[/latex] Range [latex]=(-\infty,4\rbrack[/latex]
  5. [latex](0,-5)[/latex]
  6. The points are symmetric across the axis of symmetry.

Graph B

  1. [latex]x=-2[/latex]
  2. [latex](-2,-5)[/latex]
  3. maximum
  4. D [latex]=\left(-\infty,\infty\right);[/latex] R [latex]=\lbrack-5,\infty)[/latex]
  5. [latex](0,-1)[/latex]
  6. The points are symmetric across the axis of symmetry.
  1. A Cartesian coordinate plane with evenly spaced tick marks along both axes. An upward-opening parabola has its vertex at the point (3, 4). The parabola is symmetric about the vertical line x=3, which represents its axis of symmetry.
    Up
    Axis of symmetry: [latex]x=3[/latex]
    Vertex: [latex](3,4)[/latex]
    y-intercept: [latex](0,13)[/latex]
    Number of x-intercepts: none
    Domain : [latex]\left(-\infty,\infty\right)[/latex]
    Range: [latex]\lbrack4,\infty)[/latex]
  2. A Cartesian coordinate plane with evenly spaced tick marks along both axes. A downward-opening parabola has its vertex at (-1, 0). The parabola is symmetric about the vertical line x=-1 and crosses the y-axis at the point (0, -1).
    Down
    Axis of symmetry: [latex]x=-1[/latex]
    Vertex: [latex](-1,0)[/latex]
    y-intercept: [latex](0,-1)[/latex]
    Number of x-intercepts: 1
    Domain : [latex]\left(-\infty,\infty\right)[/latex]
    Range: [latex](-\infty,0\rbrack[/latex]
  3. A Cartesian coordinate plane with evenly spaced tick marks along both axes. A downward-opening parabola has its vertex at the point (2, 7). The parabola crosses the y-axis at (0, 3) and is symmetric about the vertical line x=2.
    Down
    Axis of symmetry: [latex]x=2[/latex]
    Vertex: [latex](2,7)[/latex]
    y-intercept: [latex](0,3)[/latex]
    Number of x-intercepts: 2
    Domain : [latex]\left(-\infty,\infty\right)[/latex]
    Range: [latex](-\infty,7\rbrack[/latex]
  4. A Cartesian coordinate plane with evenly spaced tick marks along both axes. A small downward-opening parabola is located in the third quadrant. The vertex is at (-5, -7), and the parabola is symmetric about the vertical line x=-5.
    Down
    Axis of symmetry: [latex]x=-5[/latex]
    Vertex: [latex](-5,-7)[/latex]
    y-intercept: [latex](0,-82)[/latex]
    Number of x-intercepts: none
    Domain : [latex]\left(-\infty,\infty\right)[/latex]
    Range: [latex](-\infty,-7\rbrack[/latex]

Homework: Graphing Quadratic Functions

  1. Explain.
  2. A Cartesian coordinate plane with evenly spaced tick marks along both axes. An upward-opening parabola is shown in the second quadrant. The vertex is at the point (-5, 1), and the parabola is symmetric about the vertical line x=-5.
    Up
    Axis of symmetry: [latex]x=-5[/latex]
    Vertex: [latex](-5,1)[/latex]
    y-intercept: [latex](0,26)[/latex]
    Number of x-intercepts: none
    Domain : [latex]\left(-\infty,\infty\right)[/latex]
    Range: [latex]\lbrack1,\infty)[/latex]
  3. A Cartesian coordinate plane with evenly spaced tick marks along both axes. A downward-opening parabola has its vertex at (2, 8). The parabola crosses the y-axis at (0, 0) and is symmetric about the vertical line x=2.
    Down
    Axis of symmetry: [latex]x=2[/latex]
    Vertex: [latex](2,8)[/latex]
    y-intercept: [latex](0,0)[/latex]
    Number of x-intercepts: 2
    Domain : [latex]\left(-\infty,\infty\right)[/latex]
    Range: [latex](-\infty,8\rbrack[/latex]
    Explain.
  4. A Cartesian coordinate plane with evenly spaced tick marks along both axes. A downward-opening parabola has its vertex at (-4, 0) and is symmetric about the vertical line x=-4.
    Down
    Axis of symmetry: [latex]x=-4[/latex]
    Vertex: [latex](-4,0)[/latex]
    y-intercept: [latex](0,-16)[/latex]
    Number of x-intercepts: 1
    Domain : [latex]\left(-\infty,\infty\right)[/latex]
    Range: [latex](-\infty,0\rbrack[/latex]
    Explain.
  5. A Cartesian coordinate plane with evenly spaced tick marks along both axes. A downward-opening parabola has its vertex at (1, -2). The parabola crosses the y-axis at (0, -3) and is symmetric about the vertical line x=1.
    Down
    Axis of symmetry: [latex]x=-1[/latex]
    Vertex: [latex](1,-2)[/latex]
    y-intercept: [latex](0,-3)[/latex]
    Number of x-intercepts: none
    Domain : [latex]\left(-\infty,\infty\right)[/latex]
    Range: [latex](-\infty,-2\rbrack[/latex]
  6. A Cartesian coordinate plane with evenly spaced tick marks along both axes. An upward-opening parabola has its vertex at (4, -2) and is symmetric about the vertical line x=4. The parabola crosses the x-axis at the points (-3, 0) and (-4, 0).
    Up
    Axis of symmetry: [latex]x=-4[/latex]
    Vertex: [latex](4,-2)[/latex]
    y-intercept: [latex](0,30)[/latex]
    Number of x-intercepts: 2
    Domain : [latex]\left(-\infty,\infty\right)[/latex]
    Range: [latex]\lbrack-2,\infty)[/latex]
  7. Answers may vary.

Prep for Applications of Quadratic Functions

    1. meters per second
    2. 58.8 m
    3. [latex]D\left(t\right)=-4.9t^2+19.6t+58.8[/latex]
    4. The distance from the ground in meters
    5. When does the object strike the ground?
    1. feet per second
    2. height above the ground
    3. feet
    4. time
    5. seconds
    6. the graph is a parabola opening down.
    1. seconds
    2. meters
    3. seconds
    1. feet
    2. seconds
  1. Discuss
  2. exact
  3. approximate
  4. exact
  5. approximate
  6. exact
  7. approximate
  8. [latex]=[/latex]
  9. [latex]\approx[/latex]
  10. [latex]\approx[/latex]
  11. [latex]=[/latex]
  12. [latex]\approx[/latex]
  13. [latex]\approx[/latex]
  14. [latex]\approx[/latex]
  15. [latex]=[/latex]
  16. [latex]\approx[/latex]
  17. [latex]3,600[/latex]
  18. [latex]45[/latex]
  19. [latex]39.82[/latex]
  20. [latex]72.49[/latex]
  21. [latex]-3.094[/latex]
  22. [latex]0.3[/latex]
  23. [latex]0.3[/latex]
  24. [latex]0.59[/latex]

Classwork: Applications of Quadratic Functions

    1. 8 sec
    2. 256 ft
      1. 192 ft
      2. Up
      1. 192 ft
      2. Down
    5. 1 second, 7 seconds
    6. from 0 to 1 because it covered more distance.
    7. Domain [latex]=\left[0,8\right][/latex]; Range [latex]=\left[0,256\right][/latex]
    1. [latex](0,0)[/latex]
    2. Discuss
    3. Discuss
    4. x-intercept is used for domain; vertex is used for range
    1. x y
      0 23
      3 311
      6 311
      9 23
      10 −137
    2. 23 ft
    3. 311 ft
    4. 347 ft
    5. between 9 and 10 secs
    1. 2 meters
    2. [latex]2.30625[/latex] meters
    3. The ball is never above 3 meters
  5. The skateboarder is about 0.86 ft above the ground at the bottom of the half-pipe. The bottom of the half-pipe is 6.75 ft away from the starting point of the ride.
    1. 25 feet
    2. 25 feet at [latex]t=0[/latex]
    1. No, the maximum height is [latex]12.25[/latex] feet.
    2. 6 feet

Homework: Applications of Quadratic Functions

    1. x y
      0 80
      1 124
      2 136
      3 116
      4 64
      5 −20
    2. 80 ft
    3. 134 ft
    4. 136.25 ft
    5. between 4 and 5 seconds
    1. 8 feet
    2. 0.625 seconds
    3. 14.25 feet
    1. [latex](0, 0)[/latex]
    2. Discuss
    3. Discuss
    4. x-intercept is used for domain; vertex is used for range
    5. Answers may vary
    1. 33 feet
    2. 0.375 seconds
    3. 35.25 feet
    1. There are 4,540 parking spaces at 7 A.M.
    2. There are only 40 parking spaces at 10 A.M.
  6. The maximum height is 52 meters at time [latex]t=0[/latex]

Prep for Solving Using Quadratic Formula

  1. 5
  2. 10
  3. [latex]\sqrt{889}[/latex]
  4. Discuss with a classmate
  1. [latex]2\sqrt{3}[/latex]
  2. [latex]6\sqrt{2}[/latex]
  3. [latex]\frac{7 \pm \sqrt{3}}{2}[/latex]
  4. [latex]-1, 7[/latex]
  5. [latex]1 \pm \sqrt{5}[/latex]
  6. [latex]\frac{5\pm\sqrt5}2[/latex]
  1. [latex]6i[/latex]
  2. [latex]6i\sqrt{2}[/latex]
  3. [latex]\frac{2}{5}i[/latex]
  4. [latex]-3 \pm \frac{3}{2}i[/latex]
  5. [latex]\frac{5}{2} \pm \frac{3\sqrt{2}}{2}i[/latex]
  6. [latex]2 \pm 3i[/latex]

Classwork: Solving Using the Quadratic Formula

  1. [latex]x = 2 \pm \sqrt{7}[/latex]
  2. [latex]x = \pm i\sqrt{3}[/latex]
  3. [latex]x = \frac{-5 \pm \sqrt{33}}{2}[/latex]
  4. [latex]x = \frac{3}{2} \pm \frac{\sqrt{11}}{2}i[/latex]
  5. [latex]x = -3[/latex]
  6. [latex]x = \frac{3 \pm \sqrt{13}}{4}[/latex]
  7. [latex]x = \frac{3 \pm \sqrt{29}}{10}[/latex]
  8. [latex]x = \frac{7}{2} \pm \frac{\sqrt{23}}{2}i[/latex]
  9. [latex]x = \pm \frac{5}{2}i[/latex]
  10. [latex]x = 4, -\frac{1}{2}[/latex]
  11. [latex]x = \frac{-1 \pm \sqrt{11}}{4}[/latex]
  12. [latex]x = \frac{9}{2}, 0[/latex]
  1. 2
  2. 1
  3. none
  4. Discuss.
  5. Check with your classmate.

A Cartesian coordinate plane with evenly spaced tick marks along both axes. A downward-opening parabola has its vertex above the x-axis at (1, 3) and is symmetric about the vertical line x=1.

  1. Down
    Axis of symmetry: [latex]x=1[/latex]
    Vertex: (1,3)
    y-intercept: (0,1)
    x-intercepts: [latex]\left(\frac{2\pm\sqrt6}2,0\right)[/latex]
    Domain: [latex]\left(-\infty,\infty\right)[/latex]
    Range: [latex](-\infty,3\rbrack[/latex]
    1. 293 feet
    2. 329 feet
    3. 2 seconds, 7 seconds
    4. 9.03 seconds
    5. Domain [latex]=[0,9.03][/latex]; Range [latex]=[0,329][/latex]
  2. The will hit the ground in approximately 2.33 sec

Homework: Solving Using the Quadratic Formula

  1. [latex]5\sqrt{7}[/latex]
  2. [latex]3 \pm \frac{\sqrt{3}}{2}[/latex]
  3. [latex]10i\sqrt{3}[/latex]
  4. [latex]5 \pm \frac{i\sqrt{30}}{2}[/latex]
  1. [latex]x = \frac{7}{2}, -\frac{5}{3}[/latex]
  2. [latex]x = \frac{17}{20}, -\frac{10}{29}[/latex]
  3. [latex]x = \frac{5 \pm \sqrt{109}}{6}[/latex]
  4. [latex]x = \pm \frac{\sqrt{2}}{4}[/latex]
  5. [latex]x = 4 \pm \sqrt{6}[/latex]
  6. [latex]x = -\frac{3}{4} \pm \frac{\sqrt{51}}{4}i[/latex]
  7. [latex]x = \frac{1}{3} \pm \frac{\sqrt{71}}{3}i[/latex]
  8. [latex]x = 1[/latex]
  9. [latex]x = \frac{5 \pm \sqrt{17}}{2}[/latex]
  10. [latex]x = 0, 2[/latex]
  11. Explain.
  12. Discuss.
  13. Check with a classmate.

A Cartesian coordinate plane with evenly spaced tick marks along both axes. A downward-opening parabola has its vertex above the x-axis at (3, 3) and is symmetric about the vertical line x=3.

  1. Down
    Axis of symmetry: [latex]x=3[/latex]
    Vertex: (3,3)
    y-intercept: (0,-15)
    x-intercepts: [latex]\left(\frac{6\pm\sqrt6}2,0\right);[/latex]
    Domain: [latex]\left(-\infty,\infty\right)[/latex]
    Range: [latex](-\infty,3\rbrack[/latex]
  1. 1.57 seconds
  2. 1.45 seconds
  3. [latex]\approx10.32[/latex] seconds longer
    1. 2 seconds
    2. 382 feet
    3. Domain [latex]=[0,4.763][/latex]; Range [latex]=[0,382][/latex]
    4. A Cartesian coordinate plane with a curved line that begins at the point (0, 382) on the y-axis and curves downward, crossing the x-axis at (4.763, 0). The curve represents a partial downward path resembling one side of a parabola. The y-axis is labeled in intervals of 80 up to 360, and the x-axis is labeled in intervals of 2 up to 8.

Classwork: Solving Using the Square Root Method

  1. [latex]x = \pm 4[/latex]
  2. [latex]x = \pm 10[/latex]
  3. [latex]x = \pm 5i[/latex]
  4. [latex]x = \pm 9i[/latex]
  5. [latex]x = \pm i\sqrt{3}[/latex]
  6. [latex]x = \pm i[/latex]
  7. [latex]x = \pm \sqrt{15}[/latex]
  8. [latex]x = \pm \frac{3\sqrt{11}}{2}[/latex]
  9. [latex]x = \pm 4[/latex]
  10. [latex]x = \pm \frac{2\sqrt{2}}{7}i[/latex]
  11. [latex]x = \pm 2\sqrt{3}[/latex]
  12. [latex]x = \pm \sqrt{41}[/latex]
  13. [latex]x = \pm \sqrt{3}[/latex]
  14. [latex]x = \pm \sqrt{23}[/latex]
  15. [latex]x = \pm 8[/latex]
  16. [latex]x = \pm \frac{2}{3}i[/latex]
  1. 1.25 seconds
  2. [latex]x=\pm\frac{\sqrt5}3[/latex]
  3. Explain.
  4. Discuss.

Homework: Solving Using the Square Root Method

  1. Many answers possible.
  1. [latex]x = \pm 7[/latex]
  2. [latex]x = \pm \sqrt{3}[/latex]
  3. [latex]x = \pm 2i[/latex]
  4. [latex]x = \pm \frac{9}{2}i[/latex]
  5. [latex]x = \pm \sqrt{46}[/latex]
  6. [latex]x = \pm 2\sqrt{7}[/latex]

A Cartesian coordinate plane with evenly spaced tick marks along both axes. An upward-opening parabola has its vertex at (0, -5) and is symmetric about the vertical line x=0.

  1. Up
    Axis of symmetry: [latex]x=0[/latex]
    Vertex:[latex](0,-5)[/latex]
    y-intercept: [latex](0,-5)[/latex]
    x-intercepts: [latex]\left(\pm\frac{\sqrt5}2,0\right)[/latex]
    Domain:[latex]\left(-\infty,\infty\right)[/latex]
    Range: [latex]\lbrack-5,\infty)[/latex]
  1. 3.26 seconds
  2. Answers may vary
  3. Many answers possible.

Prep for Solving Equations by Factoring

  1. [latex]10(y^2 + 1)[/latex]
  2. [latex]3t(t + 2)[/latex]
  3. [latex]3x^2(5 - 7x^3)[/latex]
  4. [latex]6x^4(4 + 5x^3)[/latex]
  5. [latex]6(x^2 - 4x + 5)[/latex]
  6. [latex]2x(4x^2 + 6x - 5)[/latex]
  7. [latex](5x + 2y)(3z + 4)[/latex]
  8. [latex](6x^2 + 5)(4x - 7)[/latex]
  9. [latex]3x(x - 1)(y - 2)[/latex]
  10. [latex](3x - 2)(3y + 10x)[/latex]
  11. [latex]2(4x - 5)(7x + 3y)[/latex]
  12. [latex](4x - 5)(2y + 3)[/latex]
  1. [latex](x - 2)(x - 4)[/latex]
  2. [latex](x + 1)(x - 15)[/latex]
  3. [latex](x - 4)(x + 7)[/latex]
  4. [latex](x - 3)^2[/latex]
  5. [latex](x + 5)(x - 2)[/latex]
  6. [latex](x - 5)(x + 3)[/latex]
  7. [latex]7(x - 5)(x - 1)[/latex]
  8. [latex]3(x + 4)(x - 2)[/latex]
  9. [latex](2x - 1)(3x + 2)[/latex]
  10. [latex](5x - 4)(x - 2)[/latex]
  11. [latex](3x - 2)(x + 5)[/latex]
  12. Prime
  13. [latex](4x - 3)(2x + 3)[/latex]
  14. [latex](5x + 7)(2x + 1)[/latex]
  15. [latex](x - 2)(3x + 1)[/latex]
  16. [latex](3x - 2)(4x + 3)[/latex]
  1. [latex](x + 7)(x - 7)[/latex]
  2. [latex](2x + 9)(2x - 9)[/latex]
  3. Prime
  4. [latex]2x(4x + 1)(4x - 1)[/latex]
  5. [latex]25(x^2 + 4)[/latex]
  6. [latex](7 - x)(7 + x)[/latex]
  7. [latex]x(x + 1)(x - 1)[/latex]
  8. [latex]3x(x + 2)(x - 2)[/latex]

Classwork: Solving Equations by Factoring

  1. [latex]x = \frac{4}{3}, -\frac{4}{3}[/latex]
  2. [latex]x = -7, -1[/latex]
  3. [latex]x = -3, -\frac{1}{2}[/latex]
  4. [latex]x = 3[/latex]
  5. [latex]x = -\frac{5}{2}, 0[/latex]
  6. [latex]t = -3, -6[/latex]
  7. [latex]x = 0, \frac{1}{2}[/latex]
  8. [latex]x = -2, \frac{3}{4}[/latex]
  9. [latex]x = -\frac{1}{5}, -\frac{8}{5}[/latex]
  10. [latex]x = -2, 2[/latex]
  11. [latex]x = 8, -8[/latex]
  12. [latex]t = \frac{7}{4}, -\frac{7}{4}[/latex]
  13. [latex]x = 2, \frac{3}{4}[/latex]
  14. [latex]x = -\frac{5}{3}, -\frac{6}{5}[/latex]
  15. [latex]x = 5, -\frac{7}{2}[/latex]
  16. [latex]t = \frac{3}{2}, -\frac{8}{3}[/latex]
  17. [latex]x = -\frac{3}{2}, \frac{25}{6}[/latex]
  18. [latex]x = \frac{2}{5}, \frac{1}{3}, 0[/latex]
  19. [latex]x = \frac{7}{3}, \frac{4}{3}[/latex]
  20. [latex]x = 0, -\frac{3}{4}, \frac{3}{2}[/latex]
  21. [latex]t = -\frac{1}{3}, \frac{2}{5}[/latex]
  22. [latex]x = -\frac{3}{4}, \frac{2}{3}[/latex]
  23. [latex]x = 3, \frac{2}{7}[/latex]
  24. [latex]x = -4, -\frac{1}{6}[/latex]
  25. [latex]x=-\frac49,\frac49[/latex]
  26. [latex]x = 2, -2[/latex]

A Cartesian coordinate plane with evenly spaced tick marks along both axes. An upward-opening parabola has its vertex at (-2, -8) and is symmetric about the vertical line x=-2. The parabola crosses the x-axis at (0, 0) and (-4, 0), and the y-intercept is also at (0, 0).

  1. Up
    Axis of symmetry:[latex]x=-2[/latex]
    Vertex:[latex](-2,-8)[/latex]
    y-intercept:[latex](0, 0)[/latex]
    x-intercepts:[latex](0, 0),(-4, 0)[/latex]
    Domain: [latex]\left(-\infty,\infty\right)[/latex]
    Range: [latex]\lbrack-8,\infty)[/latex]
    1. 8 second, 7 seconds
    2. 1
  2. [latex]x=0,-3[/latex]
  3. Explain.

Homework: Solving Equations by Factoring

  1. [latex]x = -3, -5[/latex]
  2. [latex]t = \pm \frac{5}{2}[/latex]
  3. [latex]x = \frac{5}{3}, -\frac{3}{2}[/latex]
  4. [latex]x = 0, -10[/latex]
  5. [latex]t = -\frac{3}{2}[/latex]
  6. [latex]x = 6, -\frac{1}{4}[/latex]
  7. [latex]x = \frac{4}{3}[/latex]
  8. [latex]x = -\frac{4}{3}, 3[/latex]
  9. [latex]x = 0, -6, 2[/latex]
  10. [latex]x = -\frac{2}{3}, -\frac{4}{3}[/latex]
  11. [latex]x = 0, \frac{1}{5}[/latex]
  12. [latex]t = -3, -\frac{3}{2}[/latex]
  13. [latex]t = 4, \frac{3}{5}[/latex]
  14. [latex]x = 0, \pm \frac{3}{2}[/latex]
  15. [latex]x = -6, \frac{1}{4}, 0[/latex]
  16. [latex]x = -\frac{5}{2}, 1[/latex]
  17. [latex]x = 0, \frac{1}{4}[/latex]
  18. [latex]x = 5, -5[/latex]
  19. [latex]t = \frac{4}{5}, -\frac{2}{3}[/latex]
  20. [latex]x = -\frac{5}{2}, \frac{3}{4}[/latex]
  21. Answers may vary.

A Cartesian coordinate plane with evenly spaced tick marks along both axes. A downward-opening parabola has its vertex at (0, 1) and is symmetric about the vertical line x=0. The parabola crosses the x-axis at (-1, 0) and (1, 0), and the y-intercept is at (0, 1).

  1. Down
    Axis of symmetry: [latex]x=0[/latex]
    Vertex: [latex](0,1)[/latex]
    y-intercept: [latex](0,1)[/latex]
    x-intercepts: [latex](-1,0),(1,0)[/latex]
    Domain: [latex]\left(-\infty,\infty\right)[/latex]
    Range: [latex](-\infty,1\rbrack[/latex]
    1. 1 seconds, 3 seconds
    2. 5 seconds
  2. Answers may vary.
  3. Explain.

 

License

Icon for the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License

College Algebra for Non-STEM Majors Copyright © by Northwest Vista College Mathematics Department is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

Share This Book