How do you find the axis of symmetry, and the maximum or minimum value of the function #y = −3x^2 − 12x + 5#?

1 Answer
Meave60
Jan 23, 2016

The axis of symmetry is #x=-2#.
The vertex is #(-2,17)#.

Explanation:

#y=-3x^2-12x+5# is in standard form, #ax^2+bx+c#, where #a=-3, b=-12, and c=5"#.

The axis of symmetry is an imaginary vertical line that separates the parabola into two equal halves. The formula for the axis of symmetry is #x=(-b)/(2a)#.

#x=(-(-12))/(2*-3)=#

#x=12/(-6)=#

#x=-2#

This is also the #x# value of the vertex, which is the maximum point of this parabola. We can know that the vertex is the maximum point because when #a<0#, the parabola opens downward.

To find the #y# value for the vertex, substitute #-2# for #x# in the equation and solve for #y#.

#y=-3x^2-12x+5#

#y=-3(-2)^2-12(-2)+5=#

#y=-3(4)+24+5=#

#y=-12+24+5=#

#y=17#

The vertex is #(-2,17)#.

graph{y=-3x^2-12x+5 [-9.64, 10.36, 7.694, 17.69]}

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