How do you find the axis of symmetry, and the maximum or minimum value of the function #y = 2x^2 + 24x + 62#?

1 Answer
Nov 12, 2017

Axis of symmetry is #x+6=0# and mimima occurs at #x=-6#, when the value of function is #-10#.

Explanation:

Let us first convert te equation to vertex form i.e. #y=a(x-h)^2+k#. The maxima or minima of such a function depends on #a#. If it is positive then we have a minima and if #a# is negative we have a maxima.

In such a equation, #(h,k)# is vertex and indicates that maxima / minima occurs when #x=h# and the value of function then is #k#. Further, #x-h=0# is the axis of symmetry.

Now we have #y=2x^2+24x+62#

i.e. #y=2(x^2+12x+31)#

or #y=2(x^2+12x+36-5)#

or #y=2(x+6)^2-10#

Hence axis of symmetry is #x+6=0# and mimima occurs at #x=-6#, when the value of function is #-10#.

graph{2x^2+24x+62 [-13.05, 6.95, -11.16, -1.16]}