Algebra 2 Honors
Parabola Review
Mrs. Schempp
Name______________________________________________
Period ____________ Date __________________________
Graph each parabola. Identify the vertex, axis of symmetry, direction of opening, zeros, and y -intercept.
1
1. 𝑓(𝑥) = (𝑥 + 1)2 − 2
3. 𝑓(𝑥) = −2(𝑥 + 3)2 − 2
2. 𝑓(𝑥) = (𝑥 − 1)2 + 2
3
Vertex:
Axis of symmetry:
Direction of opening:
Zeros:
Y- intercept
Vertex:
Axis of symmetry:
Direction of opening:
Zeros:
Y- intercept:
Vertex:
Axis of symmetry:
Direction of opening:
Zeros:
Y- intercept:
4. 𝑓(𝑥) = 𝑥 2 − 4
5. 𝑓(𝑥) = (𝑥 + 5)2
6. 𝑓(𝑥) = −(𝑥 + 1)2
Vertex:
Axis of symmetry:
Direction of opening:
Zeros:
Y- intercept:
Vertex:
Axis of symmetry:
Direction of opening:
Zeros:
Y- intercept:
Vertex:
Axis of symmetry:
Direction of opening:
Zeros:
Y- intercept:
Write each equation in vertex form by completing the square.
7. 𝑔(𝑥) = 2𝑥 2 + 8𝑥 + 10
8. ℎ(𝑥) = 𝑥 2 + 4𝑥 − 2
9. 𝑗(𝑥) = −𝑥 2 − 2𝑥 + 9
Use the best method to find the zeros of each quadratic. What is the vertex for each parabola?
10. 𝑓(𝑥) = 2𝑥 2 + 4𝑥 − 6
11. 𝑔(𝑥) = 4𝑥 2 − 6𝑥 + 2
12. ℎ(𝑥) = −3𝑥 2 + 6𝑥 − 3
Answer the questions about the given parabola.
13. Graph: 𝑦 = 𝑥 2 − 3
14. Reflect the graph of #13 across the
Vertex: _______________________
x-axis. What is the equation of the new
parabola?
15. Reflect the graph of #13 across the
y-axis. What is the equation of the new
parabola?
Equation: _____________________________
Equation: _____________________________
Write the equation of each parabola with the given vertex and passing through the given point. Graph each parabola.
16. V(1,-3) and (-2,0)
17. V(-2,3) and (0,4)
18. V(3, -3) and (1,1)
Equation: _____________________________
Equation: _____________________________
Equation: _____________________________
19. A ball is thrown in the air and follows the path determined by the equation 𝑓(𝑡) = −8𝑡 2 + 32𝑡 + 40 where t is measured
in seconds and f(t) is measured in feet. Analyze the equation to answer the following questions.
a. What is the maximum height achieved by the ball?
b. How many seconds does it take for the ball to reach it’s maximum height?
c. What is the minimum height that the ball will achieve?
d. How many seconds does it take for the ball to hit the ground?
20. True or False? The equation for a parabola must have only one term that is squared.