Question

a) Find the equation of the parabola with vertex (2,5) which also passes through the point (4, -3)

Answer 1

In order to find the equation of the parabola, let's use the vertex form below:

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

Where the vertex is located at (h, k). If the vertex is located at (2, 5), therefore h = 2 and k = 5.

Now, let's use the point (4, -3) in the equation so we can calculate the value of a:

$\begin{gathered} y=a(x-2)^2+5\\ \\ -3=a(4-2)^2+5\\ \\ -3=4a+5\\ \\ 4a=-8\\ \\ a=-2 \end{gathered}$

Therefore the equation is:

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