Question

What is the equation of the graphed function?

Enter your answer in the box.

f(x)=

Answer 1

`\large\boxed{y=(x+3)^2=x^2+6x+9}`

Explanation:

It's the parabola - the graph of a quadratic function.

The vertex form of an equation of a parabola:

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

(h, k) - vertex

We have the vertex in (-3, 0) → h = -3, k = 0. Substitute:

`y=a(x-(-3))^2+0\\\\y=a(x+3)^2`

Choice one point from the graph (-1, 4). Substitute:

`4=a(-1+3)^2\\\\4=a(2)^2`

`4=a(4)` divide both sides by 4

`1=a\to a=1`

Finally:

`y=(x+3)^2=x^2+6x+9`

`_{\text{used}\ (a+b)^2=a^2+2ab+b^2}`