Question

the graph of $g(x)=(x - 5)^2 - 35$ is a transformation of $f(x)=x^2$. how does the $y$-intercept of $g(x)$ relate to the $y$-intercept of $f(x)$?
enter your answers in the boxes.
the $y$-intercept of $g(x)=(x - 5)^2 - 35$ is at $(square,square)$. this represents a vertical shift of $square$ unit(s) down from the $y$-intercept

Explanation:

Step1: Find y-intercept of $f(x)$

Set $x=0$ in $f(x)=x^2$:
$f(0)=0^2=0$
So y-intercept of $f(x)$ is $(0,0)$.

Step2: Find y-intercept of $g(x)$

Set $x=0$ in $g(x)=(x-5)^2-35$:
$g(0)=(0-5)^2-35=25-35=-10$
So y-intercept of $g(x)$ is $(0,-10)$.

Step3: Calculate vertical shift

Subtract y-value of $f(x)$ intercept from $g(x)$:
$-10 - 0 = -10$ (negative means shift down 10 units)

Answer:

The y-intercept of $g(x)=(x-5)^2-35$ is at $\boldsymbol{(0,-10)}$. This represents a vertical shift of $\boldsymbol{10}$ unit(s) down from the y-intercept of $f(x)$.