Quadratic Functions - Question Set 4

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The general equation for this section is y = a(x-p)2+q.

1. In the table below, fill in the values:

Equation a p q y-intercept Vertex Max/Min
y = 4(x-3)2+1
y = -2(x+1)2+4
y = -2(x-7)2-1
y=4(x+3)2-2

2. How does the value of p in the equation help you to find the vertex of the parabola?

3. How does the value of q in the equation help you to find the vertex of the parabola?

4. What effect does a have:

on the shape of the parabola?
on the orientation of the parabola?

5. If the vertex is a maximum point what is true of a?

6. If the vertex is a minimum point what is true of a?

7. How can you tell from the range of y values in the table, where your vertex is?

8. Fill in the chart for the quadratic functions that have the following characteristics:

Equation a p q y-intercept Vertex Max/Min

2
5
-2

-3
-2
5

5
-1
0

-1
0
-4

9. Write the equation for a quadratic function that:

has vertex (3,-2), opens upward and has y-intercept 7
has vertex (2,0), opens downward and has y-intercept -8.