How do you find the axis of symmetry, graph and find the maximum or minimum value of the function # y=-3x^2#?

1 Answer
Jul 23, 2018

Maximum at #(0, 0)#; axis of symmetry at #x = 0#

Explanation:

Given: #y = -3x^2#

When the equation is in #y = Ax^2 + Bx + C = 0# form:

The vertex is #(-B/(2A), f(-B/(2A)))# and

the axis of symmetry is #x = -B/(2A)#

#-B/(2A) = -0/-3 = 0#

#f(0) = -3(0^2) = 0#

Maximum is at the vertex #(0, 0)#, axis of symmetry #x = 0#

To find more points, use point plotting. Since #x# is the independent variable, select any #x# and calculate the corresponding #y#:

#ul(" "x" "|" "y" ")#
#" "-2" "|-12#
#" "-1" "|-3#
#" "1" "|-3#
#" "2" "|-12#

Graph of #y = -3x^2#:

graph{-3x^2 [-5, 5, -15, 5]}