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 \\ (50)/(100)=(100a)/(100) \\ a=(1)/(2) \end{gathered}`

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

`y=(1)/(2)(x-4)^2-5`