Question

The equation of a parabola is y = –5x(squared)–15x–31. Write the equation in vertex form

Answer 1

For a equation of the form:

$y=ax^2+bx+c$

The vertex form is given by:

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

Where:

$\begin{gathered} h=-\frac{b}{2a} \\ k=y(h) \end{gathered}$

so:

For:

$\begin{gathered} y=-5x^2-15x-31 \\ a=-5 \\ b=-15 \\ c=-31 \end{gathered}$$\begin{gathered} h=-\frac{(-15)}{2(-5)}=-\frac{3}{2}=-1.5 \\ k=-5(-1.5)^2-15(-1.5)-31=-\frac{79}{4}=-19.75 \end{gathered}$

Therefore, the vertex form of the equation is:

$\begin{gathered} y=-5(x+\frac{3}{2})^2-\frac{79}{4} \\ or \\ y=-5(x+1.5)^2-19.75 \end{gathered}$