How do you find the axis of symmetry, and the maximum or minimum value of the function #y = –3(x + 7)^2 – 10#?

1 Answer
Mar 2, 2017

#color(purple)("Thus the vertex is a maximum")#
#color(purple)("Vertex"->(x,y)=(-7,-10))#
#color(purple)("Axis of symmetry "->x=-7)#

Explanation:

This is the vertex form of equation type #y=ax^2+bx+c#

If you were to square the brackets and multiply by the -3 the #x^2# term would be #-3x^2#. As this is negative the graph is of general shape #nn#. #color(purple)("Thus the vertex is a maximum")#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The coordinates of the vertex can be read directly from the given equation but you will need to 'tweak' it a bit.

Given: #y=-3(xcolor(red)(+7))^2color(green)(-10)#

#x_("vertex")=(-1)xxcolor(red)(+7) =-7#

#y_("vertex")=color(green)(-10)#

#color(purple)("Vertex"->(x,y)=(-7,-10))#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The axis of symmetry passes through the vertex and is parallel to the x-axis (for a quadratic in x as is this one)

#color(purple)("Axis of symmetry "->x=-7)#

Tony B