Question

What is the equation of the graph below?

A graph shows a parabola that opens up with a vertex at three comma negative two.

Answer 1

Answer:

$y=(x-3)^2-2$

Step-by-step explanation:

Given vertex of parabola $(3,-2)$

Where $(h,k)$ is the vertex.

$(h,k)=(3,-2)\\h=3\ and\ k=-2$

Also parabola opens up.

The equation of parabola with vertex $(h,k)$

$y= a(x - h)^2 + k$

If $a>0$ parabola opens up.

$a<0$ parabola opens down.

As the parabola opens up the value of $a$ will greater than zero.

Plugging vertex of parabola in equation $y= a(x - h)^2 + k$

$y= a(x - 3)^2 -2$

Let us plug $a=1$

The equation will be $y= a(x - 3)^2 -2$