# What is the maximum value that the graph of -3x^2 - 12x + 15?

Jan 29, 2017

See explanation.

#### Explanation:

This is a quadratic function with a negative coefficient of ${x}^{2}$, so it reaches its maximum value at the vertex of the parabola.

Its coordinates can be calculated as:

and

## $q = - \frac{\Delta}{4 a}$

but you can also calculate $q$ by substituting $p$ to the function's formula:

$p = \frac{12}{- 6} = - 2$

$q = f \left(- 2\right) = - 3 \cdot {\left(- 2\right)}^{2} - 12 \cdot \left(- 2\right) + 15$

$q = - 3 \cdot 4 + 12 \cdot 2 + 15 = - 12 + 24 + 15 = 27$

The maximum value is $27$ at $x = - 2$