Question

Given the following function, find:
(a) vertex, (b) axis of symmetry, (c) intercepts, (d) domain, (e) range,
(f) intervals where the function is increasing,
(g) intervals where the function is decreasing, and
(h) the graph of the function. Please show all of your work.
f(x)=-3x^2+12x

Answer 1

\[ax^2 + bx + c = y\]
A) The x-coordinate of a parabola's vertex can be found by\[x = \frac {-b}{2a}\] After you solve for x, plug it into the equation to find the y-coordinate.
B) Axis of symmetry is just the x = -b/2a
C) Y-intercepts can be found by plugging in 0 to for x. X-int can be found by plugging in 0 for f(x)
D) Domain for this type of parabola is all real.
E) Range is from the y coordinate of the vertex to +/- infinity, depending on if the parabola has a min or a max.

Answer 2

For f,g,h, first graph the parabola, then just give the intervals of where the function increases or decreases.

Answer 3

x=-12/2(-3) = 2

f(2)=-3(2)^2+(12)2
=12

vertex = (2,12)

f(0)=-3(0)^2+(12)0
=0

y-int = (0,0)

f(x)=(-3x^2+12x)=3x(x+4)
x= 0 or -4

x - int =(0,0) (-4,0)

\[(-\infty,2) (2,\infty)\]