Download 9 Review

9 Review
Short Answer
1. Without graphing, tell whether the point (2, –18) is on the graph of
.
2. Without graphing, tell whether the point (–5, 8) is on the graph of
.
3. Use a table with values x = {–2, –1, 0, 1, 2} to graph the quadratic function y = 3 x2.
4. Tell whether the graph of the quadratic function
opens upward or downward. Explain.
5. Identify the vertex of the parabola. Then give the minimum or maximum value of the function.
y
10
8
(3, 6)
6
4
2
–10 –8
–6
–4
–2
–2
2
4
6
8
10
x
6
8
10
x
–4
–6
–8
–10
6. Find the domain and range.
y
10
8
6
4
2
–10 –8
–6
–4
–2
–2
–4
–6
2
4
(3, –5)
–8
–10
7. Find the zeros of the quadratic function
from the graph.
y
10
8
6
4
2
–10 –8
–6
–4
–2
–2
2
4
6
8
10
x
–4
–6
–8
–10
8. Find the axis of symmetry of the parabola.
y
10
8
6
4
2
–10 –8
–6
–4
–2
–2
2
4
6
8
10
x
–4
–6
–8
–10
9. Find the axis of symmetry of the graph of
10. Find the vertex of the parabola
.
.
11.The trajectory of a potato launched from a potato cannon on the ground at an angle of 45 degrees with an initial speed of
65 meters per second can be modeled by the parabola:
x – 0.0023x2, where the x-axis is the ground. Find
the height of the highest point of the trajectory and the horizontal distance the potato travels before hitting the
ground.
y
220
200
180
Height (m)
160
140
120
100
80
60
40
20
20
40
60
80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500 520 540
x
Horizonal Distance (m)
12. Graph y = –x2 – 4x – 3.
13. The height of a soccer ball that is kicked from the ground can be approximated by the function
, where y is the height of the soccer ball in feet x seconds after it is kicked. Graph this function. Find the time it
takes the soccer ball to reach its maximum height, the soccer ball’s maximum height, and the time it takes the
soccer ball to return to the ground.
14. Solve the equation x2 + 2x – 3 = 0 by graphing the related function.
15. Solve the equation
16. Find the roots of
by graphing the related function.
.
17. A soccer goalie kicks the soccer ball. The quadratic function
gives the time t seconds after the
soccer ball is at height 0 feet. How long does it take for the soccer ball to return to the ground?
18. A kicker starts a football game by “kicking off”. The quadratic function
height after x seconds. How long is the football in the air?
19. Use the Zero Product Property to solve the equation
20. Solve the quadratic equation
21. Solve the quadratic equation
by factoring.
by factoring.
models the football’s
.
22. The height of an arrow that is shot upward at an initial velocity of 40 meters per second can be modeled by
, where h is the height in meters and t is the time in seconds. Find the time it takes for the arrow to
reach the ground.
23. Solve
by using square roots.
24. Solve 64x2 – 121 = 0 by using square roots.
25. Solve
. If necessary, round to the nearest hundredth.
26. Marianna is making a piñata that has a ball-like shape. The piñata has a surface area of 60 square feet. Use the
formula for the surface area of a sphere (
) to find the radius of the piñata.
27. Complete the square for
28. Solve
29. Solve
to form a perfect square trinomial.
by completing the square.
by completing the square.
30. A gardener wants to create a rectangular vegetable garden in a backyard. She wants it to have a total area of 120
square feet, and it should be 12 feet longer than it is wide. What dimensions should she use for the vegetable
garden? Round to the nearest hundredth of a foot.
31. Solve
by using the Quadratic Formula.
32. Solve 3x2 – 6x + 1 = 0 by using the Quadratic Formula. If necessary, round to the nearest hundredth.
33. Solve
.
34. Find the number of solutions of the equation
35. Find the number of x-intercepts of
by using the discriminant.
by using the discriminant.
36. Workers preparing for the city’s Fourth of July celebration shoot an object straight up with an initial velocity of
210 ft/s2 from a height of 3 feet above the ground. Will the object reach a height of 670 feet 0, 1, or 2 times? Use
the equation
where v is the initial velocity in feet per second and c is the initial height in feet
of the object above the ground. Use the discriminant to explain your answer.