3.1.1 Prep

Answer the following.

1. 1. How many x-intercepts are shown?
   2. List all x-intercepts shown.
   3. Does the graph cross or bounce off the x-axis at each x-intercept?

2. 1. How many x-intercepts are shown?
   2. List all x-intercepts shown.
   3. Does the graph cross or bounce off the x-axis at each x-intercept?

3. 1. How many x-intercepts are shown?
   2. List all x-intercepts shown.
   3. Does the graph cross or bounce o the x-axis at each x-intercept?

4. 1. How many x-intercepts are shown?
   2. List all x-intercepts shown.
   3. Does the graph cross or bounce o the x-axis at each x-intercept?

5. Solve by factoring. [latex]2x^2-5x-3=0[/latex]
6. Work backwards to write a quadratic equation in factored form with the given solutions.

   [latex]x =-2[/latex]   [latex]x = 9[/latex]

   [latex]x + 2 = 0[/latex]   [latex]x\_\_\_\_= 0[/latex]

   [latex]\left(\_\_\_\_\_\_\_\_\_\_\_\_\right)\;\;\left(\_\_\_\_\_\_\_\_\_\_\_\_\_\right)\;=0[/latex]

Write a quadratic equation in factored form with the given solutions.

7. [latex]x=-3\;\text{and}\;x=8[/latex]
8. [latex]x=0\;\text{and}\;x=5[/latex]
9. [latex]x=4\;\text{and}\;x=-\frac7{10}[/latex]
10. [latex]x=2\;\text{and}\;x=2[/latex]
11. [latex]x=\frac23\;\text{and}\;x=-\frac1{2}[/latex]
12. [latex]x=-4\;\text{and}\;x=\frac3{5}[/latex]

3.1.2 Classwork

For each graph below, answer the following.

1. How many real roots are shown in the graph?
2. What is the minimum possible degree of the polynomial if it has only the real roots shown?
3. Write a possible equation for the function in factored form with the minimum degree.

3.1.3 Homework

For each of the following, use the x-intercepts to match the equation to its graph.

1. [latex]f(x)\;=\;x^2(x-3)[/latex]
2. [latex]f(x)\;=-2x(x+2)(x-2)[/latex]
3. [latex]f(x)\;=-2{(x+3)}^{2}\;{(x+1)}^2[/latex]
4. [latex]f(x)\;=\;x[/latex]
5. [latex]f(x)\;=\;(x-1)(x-3)(x-5)[/latex]
6. [latex]f(x)\;=-x(x+3)(x-3)[/latex]
7. [latex]f(x)\;=\;x^2(x-2)(x-4)[/latex]
8. [latex]f(x)\;=-2x^2+16x-24[/latex]
9. [latex]f(x)\;=\;3x(x+1){(x-1)}^2[/latex]
10. [latex]f(x)\;=9-4x^2[/latex]
11. [latex]f(x)\;=-(x-4)(x-3){(x-1)}^2[/latex]
12. [latex]f(x)\;=-5[/latex]
13. [latex]f(x)\;=\;x^3(x-3)[/latex]
14. [latex]f(x)\;=-3(x-1){(x-2)}^2(x-3)[/latex]