Answer: [tex]y=-2(x+3)^2-2[/tex]
Explanation:
A general form of a parabola is as follows:
[tex]y=a(x-x_0)^2+y_0[/tex]
where the point [tex](x_0,y_0)[/tex] is the vertex. We know that is (-3,-2), so:
[tex]y=a(x+3)^2-2[/tex]
The remaining unknown is the coefficient "a" and we determine it using the extra point given at (-5,-10). The parabola equation must satisfy this point otherwise the point cannot lie on the parabola:
[tex]-10=a(-5+3)^2-2\\-10=4a-2\\\rightarrow a=-2[/tex]
And so we obtain the equation of the parabola:
[tex]y=-2(x+3)^2-2[/tex]
