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serious [3.7K]
3 years ago
7

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

Mathematics
1 answer:
nataly862011 [7]3 years ago
5 0
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 
\frac{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= \frac{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

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