Algebra 1
Ch.10 Review– Graphing Quadratic Functions
Name ___________________________
Match each graph with its function.
__________ 1.
y = 2x2
__________ 2.
y = x2 – 1
__________ 3.
y = –x2
__________ 4.
y = -3x2 + 2
Describe the changes of each equation from y  x 2 . (flip, wider, narrower, shift left – right - up - down)
5)
y  ( x  2) 2  4
6)
y  ( x  5) 2
7)
y  3x 2  2
Explain what the change was and write an equation. The dotted line is the original graph.
8)
9)
State whether the graph will have a maximum or minimum point.
10)
y  2( x  3) 2  4 ___________________
11)
y  x 2  5 ___________________
Graph each function.
12)
y  ( x  1) 2  3
Vertex: _________
13) y = –(x - 2)2 + 5
Graph each inequality. Don’t forget to shade.
14) y > x2 - 2
Change the equation from Standard Form to Vertex Form.
16)
y  x 2  12 x  32
Find the average rate of change between x = 0 and x = 2.
17)
15) y > (x-2)2 + 3
Vertex: _________
18. The following graph models the path of a rocket being launched from a cliff.
a) What is the y-intercept? ____________
What does it mean in the context of the problem?
b) What is the psoitive x-intercept? ___________
What does it mean in the context of the problem?
c) What is the maximum point of the problem? ______________
Describe what is means in the context of the problem.
d) Examine the graph from x = 3 to x = 6. Is the graph increasing, decreasing, or constant?
e) Explain why the domain of the function is restricettd from 0 to 6?
Graph. To find the zeros, you can try to factor or use the quadratic formula.
19) f ( x)  x 2  6 x  5
Vertex: ______________
y-intercept: _______
Zeros: _________ & ___________
20)
f ( x)  x 2  6 x  8
Vertex: ______________
y-intercept: _______
Zeros: _________ & ___________
Solve by using square roots.
21. 2x2 = 50
22.
x2 – 36 = 0
23. 3x2
– 27 = 0
Solve by factoring.
24.
x2 + 7x – 30 = 0
25. x  7 x  12  0
2
26. 2 x  5 x  3  0
2
Solve each equation by completing the square.
27. x2 + 8x – 48
28. x2 - 2x - 35 = 0
Find the zeros by using the quadratic formula. Round your answers to the nearest tenth.
2
2
29. x  9 x  20  0
30. x  12 x  5  0
Calculate the Discriminant for each Quadratic Equation. How many real solutions will it have?
31.
2x2 + 5x - 1
32. –3x2 + 6x
Discriminant __________
Discriminant __________
Real Solutions __________
Real Solutions __________