Question

2) Find the equation of the parabola with vertex (4,-5) and point (-6,45) on the graph.

Answer 1

To find the equation of the parabola knowing the vertex (4,-5) and a point (-6,45) you have to use the vertex form:

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

Replace the formula with:

Vertex:

h=4

k=-5

Point

x=-6

y=45

To calculate a

$\begin{gathered} 45=a(-6-4)^2-5 \\ 45=a(-10)^2-5 \\ 45=a(100)-5 \\ 45=100a-5 \\ 45+5=100a \\ 50=100a \\ \frac{50}{100}=\frac{100a}{100} \\ a=\frac{1}{2} \end{gathered}$

Now that we know the value of a we can write the equation of the parabola as:

$y=\frac{1}{2}(x-4)^2-5$