Identify the x-intercepts, vertex, and axis of symmetry of the graph of f(x)=−0.25(x+2)(x+8)

Answer 1

x intercepts are -2 and -8

as x+2 =0 and x+8 =0

axis of symmetry is the average of the intercepts: x= -5

y coordinate of the vertex = -.25(-5+2)(-5+8) = -(1/4)(-3)(3) = 9/4 = 2 1/4 = 2.25

vertex is (-5, 9/4)

Answer 2

for x-intercepts, set -0.25(x+2)(x+8)=0 , so x+2=0 or x+8=0 then x=-2 or x=-8.

for axis of symmetry, add x-intercepts and then divide by 2 so [(-2)+(-8)]/2=-5. x=-5 is axis of symmetry.

vertex x value is x value on axis of symmetry so x=-5, put x=-5 into f(x), so f(-5)= -0.25(-5+2)(-5+8)=-2.25

so vertex is (-5,-2,25)