Given: #f(x) = y = -0.5(x+4)(x-6)#

This function is a quadratic function. When #f(x) = 0# you can find the #x#-intercepts (zeros):

#f(x) = -0.5(x+4)(x-6) = 0#

#x + 4 = 0; " "x - 6 = 0#

#x = -4; " "x = 6#

**x-intercepts:** #" "(-4, 0), (6, 0)#

Put the equation into #y = Ax^2 + Bx + C = 0# form. Use FOIL to distribute:

#f(x) = -0.5 (x^2 -6x +4x -24) = -0.5 (x^2 -2x -24) = 0#

#f(x) = -0.5x^2 +x +12 = 0#

The vertex is #(-B/(2A), f(-B/(2A))), " axis of symmetry is " x = -B/(2A#

#-B/(2A) = -1/(2(-.5)) = 1#

#f(1) = -0.5 (1)^2 + 1 + 12 = 12.5#

**The vertex is** #(1, 12.5); " axis of symmetry is " x = 1#

You can do point-plotting to find additional points since #x# is the independent variable:

#ul(" "x" "|" "y" ")#

#-3" "|" "4.5#

#-2" "|" "8#

#-1" "|" "10.5#

#" "0" "|" "12#

#" "2" "|" "12#

#" "3" "|" "10.5#

#" "4" "|" "8#

graph{ -0.5(x+4)(x-6) [-10, 10, -5, 15]}