5.2 Properties of Parabolas.
y = ax2 + bx + c
y = -ax2 + bx + c
which way do they open?
which one has max and which one min?
Important points of a parabola.
y = x2 + 3x - 4
X
0
Y
Important points of a parabola.
y=
x2
+ 3x - 4
x = - b/2a
gives you half of vertex.
to find the other half,
plug it in.
x = -3/ (2*1) = -1.5
the max/min value HAPPENS here.
y = x2 + 3x - 4
the VALUE of the max/min is what you get when you plug in -1.5
y = (-1.5)2 + 3(-1.5) - 4 = -6.25
V = (-1.5, -6.25)
reflect to get other points!
Your small business determines that profits are
maximized with equation:
y = -2x2 + 15x + 5
x = workers employed
y = profits (in thousands)
what number of workers make the company most
profitable?
what is the profit?
Problems to do:
pg. 248
23, 25, 28-30, 35-39, 41-43.