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

Question

2568 views around the world

You can reuse this answer
Creative Commons License

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]}