Question

Write an equation for a parabola with x-intercepts (-1,0) and (3,0) which passes through the point (1, -20).

Answer 1

we know it's a parabola, so it has two solutions or zeros only, hell we know those zeros too, hmmm the values of (-1 , 0) and (3 , 0) means that x = 1 and x = 3, so let's use that

`\begin{cases} x=-1\implies &x+1=0\\\\ x=3\implies &x-3=0 \end{cases}\hspace{5em}a(x+1)(x-3)=\stackrel{0}{y} \\\\\\ \textit{we also know that} \begin{cases} x=1\\ y=-20 \end{cases}\qquad a(1+1)(1-3)=-20 \\\\\\ a(2)(-2)=-20\implies -4a=-20\implies a=\cfrac{-20}{-4}\implies a=5 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} 5(x+1)(x-3)=y \end{array}}~\hfill`

Check the picture below.