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

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

and

.
so


Remark: in the x-axis, if c is the midpoint of a and b, then

2.
since

and

are roots

and

3.
equalizing:



in the left side factorize a, in the left side factorize 8:
![a[(x_1)^{2}-(x_2)^{2}] =8(x_1 -x_2)](https://tex.z-dn.net/?f=a%5B%28x_1%29%5E%7B2%7D-%28x_2%29%5E%7B2%7D%5D%20%3D8%28x_1%20-x_2%29)
in the right side use the difference of squares formula:

simplify by


substitute

with 4:

a=2
Answer: C)2
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