Question

write a quadratic function whose graph has the given characteristics.X-intercepts: (-2,1)Point: (2,8)

Answer 1

If the x-intercepts are x=-2 and x=1 we have that the factorized form of the function is

`f(x)=k(x+2)(x-1)`

if we want that the point (2,8) belongs to the graph we have that

`\begin{gathered} 8=k(4)\cdot(1)=4k \\ k=2 \end{gathered}`

therefore the function is

`f(x)=2(x+2)(x-1)=2\cdot\lbrack x^2+x-2\rbrack=2x^2+2x-4`
`f(x)=2x^2+2x-4`