Question

Find the coordinates of the vertex of the following parabola algebraically. Writer answer as an (x,y) point y=-x² - 7

Answer 1

The expression we have is:

$y=-x^2-7$

We need to compare this equation of our parabola, with the general equation of a parabola in vertex form:

$y=a(x-h)^2+k$

Where (h,k) is the vertex of the parabola, and a indicates if the parabola opens up or opens down (if a is positive the parabola opens up, and if a is negative the parabola opens down).

We take our equation:

$y=-x^2-7$

And we arrange the terms so that it looks like the vertex form:

$y=(-1)(x-0)^2+(-7)$

And we can find the values of a, h, and k:

$\begin{gathered} a=-1 \\ h=0 \\ k=-7 \end{gathered}$

We only need h and k for the vertex:

$(h,k)=(0,-7)$

Answer: the vertex is at (0,-7)