Name: ___________________________________________________ 8.3 Graph y = Ax2 + Bx + C Worksheet
Fill in the requested information and use it to graph the parabolas.
1) y = –x2 + 4x – 3
2) y = x2 – 2x + 5
opens: _____
opens: ______
y–intercept: ____
y–intercept: ____
aos: _______
aos: ________
vertex: _______
vertex: ________
maximum or minimum: _____
maximum or minimum: _____
3) y = –2x2 – 8x – 5
4) y = –2x2 + 4x
opens: _____
opens: ______
y–intercept: ____
y–intercept: ____
aos: _______
aos: ________
vertex: _______
vertex: ________
maximum or minimum: _____
maximum or minimum: _____
5) y = 2x2 + 4x + 1
6) y = –x2 – 2x + 3
opens: _____
opens: ______
y–intercept: ____
y–intercept: ____
aos: _______
aos: ________
vertex: _______
vertex: ________
maximum or minimum: _____
maximum or minimum: _____
Period: ______ y
7) The suspension cables between the two towers of the
Mackinac Bridge in Michigan form a parabola that can be modeled
by y = 0.000098x2 − 0.37x + 552, where x and y are measured in feet.
x
What is the height of the cable above the water at its lowest point?
Without graphing, tell whether the function has a minimum or a maximum value. Then find the
value.
8) y = 8x2 – 8x + 6
9) y = –1/4x2 + 3x + 1
10) A homeroom is having a boys vs girls water balloon launch contest to see who can launch their
balloon higher. Information about each group’s launch is given below:
Boys
Girls
The girls’ water balloon launch
can be modeled by the equation
h = –16t2 + 80t + 5
where h is measured in feet and
t is measured in seconds. h
The boys’ water balloon
launch can be modeled
by the graph: Who won the contest? Explain.
Worked–Out Solutions Online!
f
ANSWERS:
1) up
–3
x=2
(2, 1)
max: 1
6) down
3
x = –1
(–1, 4)
max: 4
2) up
5
x=1
(1, 4)
min: 4
3) down
–5
x = –2
(–2, 3)
max: 3
7) about 203 feet above the water
8) minimum: 4
9) maximum: 10
4) down
0
x=1
(1, 2)
max: 2
5) up
1
x = –1
(–1, –1)
min: –1
10) The boys won. Their balloon went up more
than 125 feet in the air according to the
graph. The girls’ balloon only went up 105
feet in the air which was determined by
calculating the maximum value.