Question

Please show work ... I have no clue how to start this problem$y=-3(x-5)^{2} -2$
I think I have to find the vertex form

Answer 1

Answer:

The given form : $y=-3(x-5)^2 - 2$ is the vertex form of the equation

Explanation:

The vertex form of the quadratic equation is given by the general rule:

y = a(x-h)² + k where (h,k) represent the vertex of the parabola

Now, let's check the given equation:

$y=-3(x-5)^2 - 2$

By comparing this form with the general form, we will find that:

a = -3, h = 5 and k = -2

which means that point (5,-2) is the vertex of the parabola

If we want to change this to the general form, we will simply expand the bracket and solve as follows:

$y = -3(x-5)^2-2\\ \\ y = -3(x^2-10x+25) - 2\\ \\ y=-3x^2 + 30x - 75 - 2\\ \\ y=-3x^2 + 30x - 77$

Attached are the graphs of the two equations. You can note that they are the same.

Hope this helps :)