Question

1. (unit 1.5 and 3.2) type an equation in quadratic vertex form that represents the function below.

quadratic vertex form: $f(x) = a(x - h)^2 + k$
copy/paste for exponent of 2: ²

Explanation:

Step1: Identify vertex $(h,k)$

From the graph, the vertex (maximum point) is at $(-1, 2)$, so $h=-1$, $k=2$. Substitute into vertex form:
$f(x) = a(x-(-1))^2 + 2 = a(x+1)^2 + 2$

Step2: Solve for $a$ using y-intercept

The graph passes through $(0,1)$. Substitute $x=0$, $f(x)=1$:
$1 = a(0+1)^2 + 2$
$1 = a + 2$
$a = 1 - 2 = -1$

Step3: Substitute $a$ into the equation

$f(x) = -1(x+1)^2 + 2$

Answer:

$f(x) = -(x+1)^2 + 2$