Question

Explain how to determine the quadratic equation using linear factors and zeros of the graph below.

Answer 1

`f(x)=-x^2+11x-28`

Explanation:

We see that the zeroes of the graphed parabola are
`x=4` and
`x=7`, which are solutions to
`x-4=0` and
`x-7=0` respectively. We also observe that the parabola opens downward, so the leading coefficient is negative. By multiplying these two factors and negating the result, we can determine the actual function:

`f(x)=-(x-4)(x-7)\\\\f(x)=-(x^2-11x+28)\\\\f(x)=-x^2+11x-28`

Thus, the quadratic equation represented by the graph is
`f(x)=-x^2+11x-28`