Question

Find the equation of the quadratic function f whose graph is shown below.1086V681012(4, -2)(3,-5)

Answer 1

We get the following information:

`(-b)/(2a)=3\rightarrow-(b)/(a)=6\rightarrow b=-6a`

and

`\begin{gathered} 9a+3b+c=-5 \\ 16a+4b+c=-2 \end{gathered}`

So if we replace b=-6a. We get

`\begin{gathered} 9a+-18a+c=-5 \\ 16a-24a+c=-2 \\ \text{therefore} \\ -9a+c=-5 \\ -8a+c=-2 \\ \text{therefore} \\ 9a-c=5 \\ -8a+c=-2 \\ a=3 \\ \end{gathered}`

having a=3

we get that

`\begin{gathered} b=-6\cdot3=-18 \\ \text{and} \\ 27-c=5 \\ c=22 \end{gathered}`

the equation is

`f(x)=3x^2-18x+22`