Question

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

Answer 1

Answer:

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

Step-by-step 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 $f(x)=-x^2+11x-28$