How do you find the axis of symmetry, graph and find the maximum or minimum value of the function #y = x^2 - 2x - 10#?

2 Answers
Jul 8, 2017

Complete the square

Explanation:

In this case, completing the square would give you:

#y=(x-1)^2-11#

Once in this form #y=(x-p)^2+q#, the negative of p is the x coordinate of the vertex of the graph and q is the y coordinate. This means the minimum (as the coefficient of #x^2# is positive (1)) of the graph will be at ( 1 , -11 ) and the line of symmetry will pass through the x coordinate, namely #x = 1#

Jul 8, 2017

Axis of symmetry: #x=1#; minimum value #-11#

Explanation:

graph{x^2-2x-10 [-28.52, 29.22, -14.43, 14.45]}

A quadratic equation in standard form is #y=ax^2+bx+c#. In this case, #a=1#, #b=-2#, and #c=-10#.
To find the axis of symmetry, use the formula #x=-b/(2a)#.

#x=-b/(2a)#
#x=-(-2)/(2(1))#
#x=1#

The graph above shows that the parabola is an upward-facing one, so it has a minimum value. The max or min is always on the axis of symmetry, so you can substitute #x=1# into the function.

#y=x^2-2x-10#
#y=1^2-2(1)-10#
#y=-11#

So, the axis of symmetry is #x=1# and the minimum value is #-11#. You can also write the minimum as the coordinate #(1,-11)#.