Question

5. Find the equation of the quadratic function that has vertex (-1,-4) and passes through the point (-5.-36). (Hint: solve for a!!!!)

Answer 1

ANSWER

$y=-2(x+1)^2-4$

EXPLANATION

The vertex form of a quadratic equation is:

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

where (h, k) = vertex

Let us substitute the given vertex and the given point into the equation to find the value of the constant a.

That is:

$\begin{gathered} -36=a(-5-(-1))^2+(-4) \\ -36=a(-5+1)^2-4 \\ -36=a(-4)^2-4 \\ -36=16a-4 \\ 16a=-36+4=-32 \\ \Rightarrow a=\frac{-32}{16} \\ a=-2 \end{gathered}$

That is the value of the constant a. Now we can write the quadratic function using the constant a and the vertex:

$\begin{gathered} y=-2(x-(-1))^2+(-4) \\ y=-2(x+1)^2-4 \end{gathered}$

That is the function.