Sec. 8.14-8.16 Quizreview-Solving All Forms

Name:______Date: ______

Sec. 8.14-8.16 QuizReview-Solving All Forms

1-3: Quadratic equations can be solved by using square roots, by factoring, or by using the quadratic formula. Solve the three equations to find t when h(t) = 0. Use a different solution method for each equation. (Hint: Don’t forget to look for a GCF firstwhen you factor and use the quadratic formula)

1. h(t) = -12t2– 6t+ 108
/ 2. h(t) = -12t2– 96t+ 108 / 3. h(t) = -12t2 + 108

4. The above three equations were examples of equations of how long it would take to drop a TV off a roof using different parachutes and padding around the TV. Jimmy found that the TV would not break if it took longer than 2.5 seconds to hit the ground. Which equation(s) will result in the TV not breaking? How many seconds for each equation?

5. Using the equation from #2, how high

would the TV be after 0.5 seconds?

7-11: Solve using any method. (factoring, square roots, completing the square, quadratic formula). Leave answers in simplified radical form when necessary

7. -6x2+270 = -248. x2+4x = 219. -3x2– 42x = 0

10. 4x2 + 5x = 811. 2(x – 5)2 = 24

12. Write a quadratic function in standard form with roots 7 and – 4.

13. The graph of a quadratic function has a vertex of (-3, 8) and a vertical stretch of -2.

a. Write the equation of the graph in vertex form.b. Write the equation of the graph in standard form.

14. Draw an example of what the graph could look like if it has two real roots (positive discriminant), one real root (discriminant is 0), or no real roots (discriminant is negative).

TWO REAL ROOTS ONE REAL ROOT NO REAL ROOTS

15-16: Graph each of the following using the vertex, roots, and axis of symmetry. Make a table when necessary.

15. y = -x2+4x+ 5

Vertex: ______

Axis of Symmetry: ______

Roots (approximate if needed): ______

16.

Vertex: ______

Axis of Symmetry: ______

Roots (approximate if needed): ______

17. A whale jumps vertically from a pool at Sea World. The function y = -16x2 + 32xmodels the height of a whale in feet above the surface of the water after x seconds.

a. How long is the whale out of the water? (Hint: think about what the question and what part of the parabola

would this be?)

b. At what time does the whale reach its’ maximum height? (Hint: think about what part of the parabola this

would be)

c. What is the maximum height of the whale? (Hint: first identify what part of the parabola this is)