For each quadratic function below use the method of completing the square or averaging the intercepts to rewrite it in graphing form. Then, state the axis of symmetry and give the vertex of each parabola. Try to use each method at least once.a. y=x2−4x+9b. f(x)=x2−8xc. y=x2+7x−2

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Asked Oct 31, 2019
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For each quadratic function below use the method of completing the square or averaging the intercepts to rewrite it in graphing form. Then, state the axis of symmetry and give the vertex of each parabola. Try to use each method at least once.

a. y=x2−4x+9

b. f(x)=x2−8x

c. y=x2+7x−2

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Expert Answer

Step 1

Part (a):

Consider the quadratic function y = x2-4x+9, use the method of completing the square to rewrite in graphing form,

The graphing form is, y = a(x-h)2+k.

y x2-x+9
y=x2 -2(2)x*+(-2}(-2} +9
2-2(2)x+(-2)-2)+9
y=(x-2)+5
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y x2-x+9 y=x2 -2(2)x*+(-2}(-2} +9 2-2(2)x+(-2)-2)+9 y=(x-2)+5

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Step 2

The quadratic equation of form, y = ax2+bx+c.

By comparing with given function, a = 1; b= -4; c = 9.

Then the axis of symmetry is,

b
2a
-4
2x1
x = 2
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b 2a -4 2x1 x = 2

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Step 3

The vertex of the e...

b2
b
2a
4a
(-4)
-4
,9
2x1
4x1
(2,5)
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b2 b 2a 4a (-4) -4 ,9 2x1 4x1 (2,5)

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