Question

find the equation of the quadratic function g whose graph is shown below.
g(x) = □

Explanation:

Step1: Identify vertex form

Quadratic vertex form: $g(x)=a(x-h)^2+k$
Vertex $(h,k)=(0,-5)$ (lowest point on graph), so:
$g(x)=a(x-0)^2-5 = ax^2-5$

Step2: Substitute known point

Use point $(-3,-3)$:
$-3 = a(-3)^2 -5$

Step3: Solve for $a$

Simplify and isolate $a$:
$-3 = 9a -5$
$9a = -3 + 5 = 2$
$a = \frac{2}{9}$

Step4: Write final equation

Substitute $a$ back into vertex form:
$g(x)=\frac{2}{9}x^2 -5$

Answer:

$g(x)=\frac{2}{9}x^2 -5$