You have the following function:
[tex]f(x)=-4x^2+12x-9[/tex]In order to determine the zeros of the function, use the quadratic formula, given by:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]where a, b and c are coeeficients of the function f(x). In this case the value of these coefficients are:
a = -4
b = 12
c = -9
By replacing the previous values into the quadratic formula and by simplifying you obtain:
[tex]\begin{gathered} x=\frac{-12\pm\sqrt[]{(12)^2-4(-4)(-9)}}{2(-4)} \\ x=\frac{-12\pm\sqrt[]{144-144}}{-8} \\ x=\frac{-12}{-8}=\frac{3}{2} \end{gathered}[/tex]Hence, there is one zero for the given function at x=3/2
