Question

Find the equation of the parabola whose vertex is (-3,1) and goes through the point (-4,-1)Give the equation in standard form.In blank 1, type aIn blank 2, type hIn blank 3, type k

Answer 1

The Solution:

The formula for the equation of the parabola is

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

In this case,

`\begin{gathered} k=1 \\ h=-3 \\ x=-4 \\ y=-1 \end{gathered}`

Substituting these values,

`\begin{gathered} -4=a(-1-1)^2-3 \\ -4=a(-2)^2-3 \end{gathered}`
`\begin{gathered} -4=4a-3 \\ -4+3=4a \\ -1=4a \end{gathered}`

Dividing both sides by 4, we get

`a=-(1)/(4)`

Thus, the equation of the parabola is:

`\begin{gathered} x=-(1)/(4)(y-1)^2-3 \\ \text{ }x+3=-(1)/(4)(y-1)^2 \end{gathered}`
`\begin{gathered} a=-(1)/(4) \\ \\ h=-3 \\ \\ k=1 \end{gathered}`