Question

identify the following key attributes from the graph of the parabola below.
vertex: (2,0)
y-intercept:

Explanation:

Step1: Find parabola vertex form

The vertex form of a parabola is $y=a(x-h)^2+k$, where $(h,k)$ is the vertex. The vertex is given as $(2,0)$, so substitute $h=2$, $k=0$:
$y=a(x-2)^2+0 = a(x-2)^2$

Step2: Solve for $a$ using y-axis point

The parabola passes through the y-intercept point $(0, y)$. From the graph, when $x=0$, the parabola is at $y=4$. Substitute $x=0$, $y=4$:
$4=a(0-2)^2$
$4=4a$
$a=1$

Step3: Confirm y-intercept value

The y-intercept is the point where $x=0$. Substitute $x=0$ into $y=(x-2)^2$:
$y=(0-2)^2=4$
The y-intercept is the point $(0,4)$.

Answer:

$(0, 4)$