Question

Vertex of the parabola formed by taking reflection of $y=4x^2-4x+3$ along the line $y=x$ will be

• A. $(\frac{-1}{2},2)$
• B. $(\frac{1}{2},-2)$
• C. $(2,\frac{1}{2})$
• D. $(\frac{-1}{2},-2)$

Answer 1

The correct option is C $(2,\frac{1}{2})$

$y=4x^2-4x+3y=(2x-1{)}^2+2y-2=4{(x-\frac{1}{2})}^2{(x-\frac{1}{2})}^2=\frac{1}{4}(y-2)$

To get the reflected equation about the line $y=x$, we have to interchange $x$ and $y.$
Hence, we get ${(y-\frac{1}{2})}^2=\frac{1}{4}(x-2)$
Therefore, the vertex will be $(2,\frac{1}{2})$