Question

Find the vertex of the quadratic function below. Write your answer in fractional form if necessary. Do not use decimals.

Answer 1

Given quadratic expression is

$f(x)=-3x^2-4x+7$

Comparing with the general quadratic function

$f(x)=ax^2+bx+c$

We have,

$a=-3,b=-4,c=7$

So, the x coordinate of the vertex is

$\begin{gathered} -\frac{b}{2a}=-\frac{-4}{-6} \\ =-\frac{2}{3} \end{gathered}$

Now, putting the x coordinate in the equation of the given function,we have,

$\begin{gathered} f(-\frac{2}{3})=-3(\frac{4}{9})-4(-\frac{2}{3})+7 \\ =-\frac{12}{9}+\frac{8}{3}+7 \\ =\frac{75}{9} \end{gathered}$

So, the vertex of th egiven quadratic function is at

$(-\frac{2}{3},\frac{75}{9})$