Question

What is the equation of a parabola using the point (-2,-5) and x-intercepts -7 and -3??

I am in big trouble please save me

Answer 1

well, we know the parabola has x-intercepts at -7 and -3, or namely zeros, and we also know that it passes through (-2 , -5)

`\begin{cases} x=-7\implies &x+7=0\\\\ x=-3\implies &x+3=0 \end{cases} \\\\\\ a(x+7)(x+3)=\stackrel{y}{0}\implies a(x+7)(x+3)=y \\\\\\ \textit{we also know that} \begin{cases} x=-2\\ y=-5 \end{cases}\implies a(-2+7) ~~ (-2+3)~~ = ~~-5 \\\\\\ a(5)(1)=-5\implies a=\cfrac{-5}{(5)(1)}\implies a=-1 \\\\[-0.35em] ~\dotfill\\\\ -(x+7)(x+3)=y\implies -\stackrel{F~O~I~L}{(x^2+10x+21)}=y\implies \boxed{-x^2-10x-21=y}`

Check the picture below.