Answer:
[tex]f(x)=-x^2+11x-28[/tex]
Step-by-step explanation:
We see that the zeroes of the graphed parabola are [tex]x=4[/tex] and [tex]x=7[/tex], which are solutions to [tex]x-4=0[/tex] and [tex]x-7=0[/tex] 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:
[tex]f(x)=-(x-4)(x-7)\\\\f(x)=-(x^2-11x+28)\\\\f(x)=-x^2+11x-28[/tex]
Thus, the quadratic equation represented by the graph is [tex]f(x)=-x^2+11x-28[/tex]
