Question

The graph of a quadratic function is shown. What is the equation of this function in f(x) = ax²+bx+c form?

Y
(-2, 2)
-2
Complete the equation of the function: f(x) =

Answer 1

taking a peek at the quadratic graph, we can see it has a vertex at (-2 , 2) and it has a couple of points, hmmm we only need one, say we'll use (-3 , -1)

`~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{a~is~negative}{op ens~\cap}\qquad \stackrel{a~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=-2\\ k=2\\ \end{cases}\implies y=a(~~x-(-2)~~)^2 + 2\hspace{4em}\textit{we also know that} \begin{cases} x=-3\\ y=-1 \end{cases}`

`-1=a(-3-(-2))^2+2\implies -1=a(-1)^2 + 2\implies -3=a \\\\[-0.35em] ~\dotfill\\\\ y=-3(~~x-(-2)~~)^2 + 2\implies y=-3(x+2)^2 +2 \\\\\\ y=-3(x^2+4x+4)+2\implies y=-3x^2-12x-12+2 \\\\\\ ~\hfill {\Large \begin{array}{llll} y=-3x^2-12x-10 \end{array}}~\hfill`

Check the picture below.