Question

What is the equation of the graphed function? Enter your answer in the box. f(x)=

Answer 1

Answer:

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

Step-by-step 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:

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

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