Question

A parabola has a vertex at ( -1 , - 9) and a point ( - 3, -5). Find the value of a if y = a (x – h )^2 + k.

Answer 1

Given that a parabola of vertex (-1, -9) and a point (-3, -5)

Where

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

To find the value of a, we will find the equation of the parabola first

Where

`\begin{gathered} (h,k)=(-1,-9) \\ (x,y)=(-3,-5) \end{gathered}`

Substitute the values of the variable into the formula above

`\begin{gathered} y=a(x-h)+k \\ -5=a(-3-(-1))+(-9) \\ -5=a(-3+1)-9 \\ -5=a(-2)-9 \\ -5=-2a-9 \\ Collect\text{ like terms} \\ -2a=-9+5 \\ -2a=-4 \\ Divide\text{ both sides by -2} \\ (-2a)/(-2)=(-4)/(-2) \\ a=2 \end{gathered}`

Hence, the value of a is 2