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

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Answer 1 · 2017-01-29T09:20:06

See 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:

$p=-b/(2a)$

and

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

$p=12/(-6)=-2$

$q=f(-2)=-3*(-2)^2-12*(-2)+15$

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

Answer:

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

This can be checked by looking at the graph:

graph{-3x^2-12x+15 [-10, 10, -40, 40]}