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Q.
Find the maximum/minimum value of the quadratic expression $-4 x^2+12 x+9$.
Quadratic Equations
Solution:
Given: $-4 x^2+12 x+9$ which is in the form of $a x^2+b x+c$,
where $a=-4< 0$.
$ \therefore \text { Maximum value }=\frac{4 a c-b^2}{4 a} $
$ =\frac{4(-3)(9)-(12)^2}{4(-3)}=\frac{4(4)(9)+144}{4(4)}=18$