Question

7. Write the equation of the parabola. Pay close attention to the scale on both axes.

Answer 1

We can start with the equation of the parabola in vertex form, as we know the coordinates of the vector:

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

The vertex is (h,k) = (-5,2), so we get:

`y=a(x-(-5))^2+2=a(x+5)^2+2`

We can use another known point, as (-6,4) to calculate the parameter a:

`\begin{gathered} y=a(x+5)^2+2 \\ 4=a(-6+5)^2+2 \\ 4=a\cdot(-1)^2+2 \\ 4=a+2 \\ a=4-2 \\ a=2 \end{gathered}`

Now that we have no more unknown parameters, we can expland the equation to the standard form:

`\begin{gathered} y=2(x+5)^2+2=2(x^2+10x+25)+2=2x^2+20x+50+2 \\ y=2x^2+20x+52 \end{gathered}`

The equation is y=2x^2+20x+52.