Question

If $y=f\left(x\right)$ is quadratic polynomial having vertex at $(6,8),$ as shown in the figure below, then $f\left(x\right)$ is

• A. $x^2+8x-76$
• B. $x^2-10x+32$
• C. $x^2-4x-4$
• D. $x^2-12x+44$

Answer 1

The correct option is D $x^2-12x+44$

Graph of $y=x^2$ is


Now shifting the graph by $6$ units right side, we get
$\Rightarrow y={(x-6)}^2$


Now, shifting this curve upwards by $8$ units, we get
$\Rightarrow y={(x-6)}^2+8$


Hence, the required equation of the curve is
$y=(x-6{)}^2+8\Rightarrow y=x^2-12x+36+8\therefore y=x^2-12x+44$