Math 2B/3A
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
Date:
Homework 22: Graphing Quadratics from Vertex Form
1. Graph each of the following functions. Remember to show and clearly label the vertex, axis of
symmetry, y-intercept, sister point, and x-intercepts.
a. y = 2(x + 3)2 − 8
b. y = −4(x − 3)2 +16
Hint: You will need to change the scale on the graph.
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Math 2B/3A
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
Date:
2. Match the equations with the graphs below. Write the equation above the graph.
y = (x −1)2 − 4
y = −(x +1)2 + 4
y = 2(x +1)2 − 8
A.
B.
C.
D.
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y = − (x −1)2 + 6
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Math 2B/3A
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
Date:
3. a. Write two different quadratic functions that would have the vertex (2, -6).
b. Write two different quadratic functions that would have the vertex (-4, 5).
4. a. The vertex of a quadratic function is (-1, 3). Where is the axis of symmetry?
b. If the y-intercept of this function occurred at the point (0, 4), find the sister point of the yintercept.
c. Is the leading coefficient of this function positive or negative? How can you tell?
5. Graph the following function. Remember to show and clearly label the vertex, axis of
symmetry, y-intercept, sister point, and x-intercepts.
𝑦 = −3(𝑥 + 2)! + 75
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Math 2B/3A
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
Date:
6. Suppose we wanted to graph the function y = (x +1)2 + 3 .
a. Find the vertex, axis of symmetry, y-intercept, and sister point of the y-intercept. Plot them
on your graph.
b. How many x-intercepts is your graph going to have?
c. This is different from the other graphs we’ve been working with! We have two fewer points
on our graph than we normally would. To get the shape of the graph more accurate, let’s
just find any other two points on the graph by choosing x values to plug into the equation
and find their corresponding y values. Plot your two extra points and sketch the graph!
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