Name:_____________________________
Date:________ Period:_______
Graphing: Review Sheet
Ms. Anderle
Graphing: Review
Along with the graphing questions, there will be review multiple choice questions!
Complete all work on a separate sheet of paper.
1. A ball is thrown vertically upward at a velocity of 75 feet per second. After t seconds, the distance s (in
feet) of the ball from the ground is modeled by the formula s = 75t – 16t2.
a. What is the maximum height of the ball?
b. After how many seconds will the ball reach the maximum height?
c. After how many seconds will the ball hit the ground?
2. During an Independence Day fireworks show, the height h in meters of a specific rocket after t
seconds can be modeled by h = -4.9(t – 4)2 + 80. When will the rocket reach its maximum height? After
how many seconds will it reach maximum height?
3. Competitors in the 10-meter platform diving competition jump upward and outward before diving
into the pool below. The height h of a diver in meters above the pool after t seconds can be
approximated by the equation h = -4.9t2 + 3t + 10. When will the diver hit the water?
4. Graph the quadratic equation: x2 – 6x + 9 = y.
a. Find the axis of symmetry.
b. Find the vertex
c. What are the x-intercepts?
5. Graph the quadratic equation: 2x2 + 4x + 7 = y
a. Find the axis of symmetry.
b. Find the vertex.
c. Find the x-intercepts.
6. Graph the equation: (x + 4)2 + (y – 3)2 = 49
a. Find the center of the circle.
b. What is the radius?
7. Graph the equation: (x – 6)2 + (y + 1)2 = 36.
a. Find the center of the circle.
b. What is the radius?
8. Solve the following system of equations algebraically.
x2 + y2 = 25
y2 + 9x2 = 25
9. Solve the following system of equations algebraically.
y = 12x – 30
4x2 – 3y = 18
10. Solve the following system of equations graphically.
y = x2 – 2x – 1
y=x+3
11. Solve the following system of equations graphically.
y = 2x2 + 2x + 3
y–x=3
12. Solve the following quadratic inequality by graphing.
𝑦 ≤ −𝑥 2 + 4𝑥 + 2
13. Solve the following quadratic inequality by graphing.
2x2 + 4x – 5 > y
14. Solve the following system of equations graphically. (round to the nearest tenth)
y = 2x – 1
y = x2 – 5x
15. Analyze y = (x – 2)2 + 5. Then draw its graph.
16. Write a quadratic equation that transforms the graph of y = 2(x + 2)2 – 5 so that it is:
a. 6 units up.
b. 3 units down.
c. 4 units to the right
d. 5 units to the left
e. narrower
f. wider
g. opens in the opposite direction