Question

Find the equation of the quadratic function with vertex (-2,18) passing through (-5,0)?

Answer 1

Answer:

$y-18=-2(x+2)^2$

Step-by-step explanation:

Equation of the Quadratic Function

The vertex form of the quadratic function has the following equation:

$y-k=a(x-h)^2$

Where (h, k) is the vertex of the parabola that results when plotting the function, and a is a coefficient different from zero.

It's been given the vertex of the parabola as (-2,18):

$y-18=a(x+2)^2$

Now substitute the point (-5,0) and find the value of a:

$0-18=a(-5+2)^2$

Operating:

$-18=a(-3)^2$

$-18=9a$

Solving for a:

$a = -18 / 9$

a = -2

Thus, the equation of the quadratic function is:

$\mathbf{y-18=-2(x+2)^2}$