Question

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

Answer 1

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

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}`