2.6 Concept Review
Concept Review: Quadratic Equations and Functions
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- Solve [latex]5x^2-45=0[/latex] three different ways using each of our three methods for solving quadratic equations.
- Pick which method from part (a) you prefer, and briefly explain why you prefer it.
- After a rocket is launched, it follows the flight path given by the function [latex]f\left(t\right)=-16t^2+9t.[/latex]
- Find the height from which the rocket was launched.
- Find the maximum height of the rocket.
- Find when the rocket hits the ground.
- After a rocket is launched, the path of the rocket is given by the function [latex]g\left(t\right)=-16t^2+9.[/latex]
- Find the y-intercept, and describe what it represents in this problem.
- Find the vertex, and describe what it represents in this problem.
- Find the x-intercept, and describe what it represents in this problem.
- How would you explain the differences in your answers for problems 2 and 3 above in the context of time and height?
- Let [latex]f\left(x\right)=x^2-81[/latex] and [latex]g\left(x\right)=x^2+81.[/latex]
- Explain the difference between the equations [latex]f\left(x\right)=0[/latex] and [latex]g\left(x\right)=0[/latex]
- Explain how to find the solutions [latex]f\left(x\right)=0[/latex] and [latex]g\left(x\right)=0[/latex]
- Can you use all three quadratic methods to solve [latex]g\left(x\right)=0[/latex]? Why or why not?
- Solve [latex]\frac{x^2}3-\frac{35}6=\frac x2[/latex]
- When solving a quadratic equation using the quadratic formula, how many and what kind of solution(s) do you get if the discriminant (inside the square root) is
- positive?
- negative?
- zero?
- Create a quadratic equation that has solutions [latex]x=5[/latex] and [latex]x=-8[/latex]
- Create a quadratic equation that has imaginary solutions. Be sure to show work and explain your reasoning.