Question

What is the equation to a graph with the vertex -1,3 and zeros -4 and -2

Answer 1

`f(x)=x^2+6x+8`

Explanation:

We are given zeros as x=-4, x=-2

so, we can set up function as

`f(x)=a(x+4)(x+2)`

Vertex is at (-1,3)

It means that graph passes through point (-1,3)

so, we can plug x=-1 and f(x)=3

and then we can solve for 'a'

`3=a(-1+4)(-1+2)`

we get

`a=1`

now, we can plug it back

and we get

`f(x)=1(x+4)(x+2)`

now, we can simplify it

`f(x)=x^2+6x+8`