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=-(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=-((-15))/(2(-5))=-(3)/(2)=-1.5 \\ k=-5(-1.5)^2-15(-1.5)-31=-(79)/(4)=-19.75 \end{gathered}`

Therefore, the vertex form of the equation is:

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