Question

Help math please thank you

Answer 1

Answer: $y=-2(x+3)^2-2$

Explanation:

A general form of a parabola is as follows:

$y=a(x-x_0)^2+y_0$

where the point $(x_0,y_0)$ is the vertex. We know that is (-3,-2), so:

$y=a(x+3)^2-2$

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:

$-10=a(-5+3)^2-2\\-10=4a-2\\\rightarrow a=-2$

And so we obtain the equation of the parabola:

$y=-2(x+3)^2-2$