Question

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

Answer 1

\[y=a \left( x^2-\frac{ 8x }{ a }+\left( \frac{ 4 }{ a } \right)^2 \right)-\frac{ 16 }{ a }-3\]
\[=a \left( x-\frac{ 4 }{ a } \right)^2-\frac{ 16 }{ a }-3\]
\[y+\frac{ 16 }{ a }+3=\left( x-\frac{ 4 }{ a } \right)^2\]
axis of symmetry is \[x-\frac{ 4 }{ a }=0~or~ x=\frac{ 4 }{ a }\]
but x=2~is axis of symmetry
Hence \[2=\frac{ 4 }{ a }\]
a=?