Answer
(a.) $k=16$.
(b.) $y=16x^2$.
(c.) $y=400$.
Work Step by Step
$\Rightarrow y=kx^2$
Substitute $x=2$ and $y=64$.
$\Rightarrow 64=k(2)^2$
Simplify.
$\Rightarrow 64=4k$
Divide both sides by $4$.
$\Rightarrow \frac{64}{4}=\frac{4k}{4}$
Simplify.
$\Rightarrow 16=k$
Hence, the value of $k$ is $16$.
(b.) Substitute $k=16$ into the equation.
$\Rightarrow y=16x^2$.
Hence, the resulting equation is $y=16(5)^2$.
(c.) Substitute $x=5$ into the equation from part (b.).
$\Rightarrow y=16(5)^2$.
Simplify.
$\Rightarrow y=16\cdot25$.
$\Rightarrow y=400$.
Hence, the value of $y$ is $400$.
