Answer :
Answer:
[tex]y-18=-2(x+2)^2[/tex]
Step-by-step explanation:
Equation of the Quadratic Function
The vertex form of the quadratic function has the following equation:
[tex]y-k=a(x-h)^2[/tex]
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):
[tex]y-18=a(x+2)^2[/tex]
Now substitute the point (-5,0) and find the value of a:
[tex]0-18=a(-5+2)^2[/tex]
Operating:
[tex]-18=a(-3)^2[/tex]
[tex]-18=9a[/tex]
Solving for a:
[tex]a = -18 / 9[/tex]
a = -2
Thus, the equation of the quadratic function is:
[tex]\mathbf{y-18=-2(x+2)^2}[/tex]