Question

quadratic functions r and s are graphed on the same coordinate grid. the vertex of the graph of r is 13 units above the vertex of the graph of s. which pair of functions could have been used to create graphs of r and s ?
\\( r(x) = 13x^2 \\) and \\( s(x) = x^2 \\)
\\( r(x) = x^2 + 13 \\) and \\( s(x) = x^2 \\)
\\( r(x) = -13x^2 \\) and \\( s(x) = x^2 \\)
\\( r(x) = x^2 - 13 \\) and \\( s(x) = x^2 \\)

Explanation:

Step1: Recall vertex of $x^2$

The vertex of $s(x)=x^2$ is $(0,0)$.

Step2: Analyze vertical vertex shift

A vertical shift of $k$ units up is $x^2 + k$. We need $k=13$.

Step3: Match to options

Check which $r(x)$ shifts $s(x)$ up 13 units.

Answer:

B. $r(x) = x^2 + 13$ and $s(x) = x^2$