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PLEASE HELP!!!!!! The line of symmetry for the quadratic equation y = ax 2 - 8x - 3 is x = 2. What is the value of "a"?

A) -2
B) -1
C) 2

User Ashaman
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8.8k points

1 Answer

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y= ax^(2) -8x-3

1.

the line of symmetry is x=2, means that the x coordinate of the vertex is x=2.

the point x=2 is the midpoint of the roots
x_1 and
x_2.

so

(x_1+x_2)/(2)=2

x_1+x_2=4

Remark: in the x-axis, if c is the midpoint of a and b, then
c= (a+b)/(2)


2.
since
x_1 and
x_2 are roots


a(x_1)^(2) -8(x_1)-3=0 and
a(x_2)^(2) -8(x_2)-3=0

3.
equalizing:


a(x_1)^(2) -8(x_1)-3=a(x_2)^(2) -8(x_2)-3


a(x_1)^(2) -8(x_1)=a(x_2)^(2) -8(x_2)


a(x_1)^(2)-a(x_2)^(2) =8(x_1) -8(x_2)

in the left side factorize a, in the left side factorize 8:


a[(x_1)^(2)-(x_2)^(2)] =8(x_1 -x_2)

in the right side use the difference of squares formula:


a(x_1 -x_2)(x_1 +x_2) =8(x_1 -x_2)

simplify by
(x_1 -x_2)


a(x_1 +x_2) =8

substitute
(x_1 +x_2) with 4:


a*4 =8

a=2


Answer: C)2

User Mayank Ahuja
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8.4k points

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