How do you find the axis of symmetry, and the maximum or minimum value of the function f(x)= -3x^2+7x-4?

Sep 22, 2017

See the explanation: A sort of cheat approach.

Explanation:

Firstly the coefficient of ${x}^{2}$ is negative so the graph is of form $\bigcap$. Thus we have a maximum.

Write the equation as: $y = - 3 \left({x}^{2} \textcolor{red}{- \frac{7}{3}} x\right) - 4$

Thus ${x}_{\text{maximum}}$ is at $x = \left(- \frac{1}{2}\right) \times \left(\textcolor{red}{- \frac{7}{3}}\right) = + \frac{7}{6}$

Now it is just a matter of substitution to determine ${y}_{\text{maximum}}$