Question

4 - vertex form of a quadratic from vertex & point
write the equation of the function in vertex form given:
vertex (-4, -3)
point (6,17)
name:
date:

Explanation:

Step1: Recall vertex form

The vertex form of a quadratic function is $y = a(x - h)^2 + k$, where $(h,k)$ is the vertex.

Step2: Substitute vertex values

Substitute $h=-4$, $k=-3$ into the formula:
$y = a(x - (-4))^2 + (-3)$
Simplify to get $y = a(x + 4)^2 - 3$

Step3: Substitute point to find $a$

Use point $(6,17)$: substitute $x=6$, $y=17$:
$17 = a(6 + 4)^2 - 3$

Step4: Solve for $a$

Calculate $(6+4)^2=100$, so:
$17 = 100a - 3$
Add 3 to both sides: $20 = 100a$
Solve for $a$: $a = \frac{20}{100} = \frac{1}{5}$

Step5: Write final equation

Substitute $a=\frac{1}{5}$ back into the vertex form:
$y = \frac{1}{5}(x + 4)^2 - 3$

Answer:

$y = \frac{1}{5}(x + 4)^2 - 3$