Grade 9 Math Quadratic Function: word problems involving maximum

1. Quadratic Function: Word
Problems Involving Maximum

2. Mechanics of the game:
• 1. Two groups are paired. Choose 1 from the
members of the group as the representative to play
the game.
• 2. The representative will answer several questions.
Each correct answer will give the chance to move
forward.
• 3. Five different colors are assigned to 5 different
representatives.
• 4. Members of the paired group can help the
representative by telling the answer in whisper.
• 5. The first one to get 5 correct answers will reach
the teacher and get the special chip with
corresponding points in the performance task.

3. It is the Graph of
Quadratic Function
𝑦 = 𝑎𝑥2
+ 𝑏𝑥 + 𝑐?
A. Line
C. Cartesian
Plane
D. Ellipse
B. Parabola

4. If a<0 in 𝑦 = 𝑎𝑥2
+
𝑏𝑥 + 𝑐, how do you
describe the vertex of
the parabola ?
B. It is at
the origin
D. It is
positive
A. It is the
minimum point
C. It is the
Maximum point

5. What is the opening of
the parabola 𝑦 =
2𝑥2
+ 5𝑥 + 3?
C. Opens
downward
B. Opens
to the left
D. Opens to
the right
A. Opens
upward

6. Which of the following is
the vertex form of
Quadratic Function?
B.
𝑦 = 𝑎𝑥2 + 𝑏𝑥 + 𝑐
D.
𝑦 = 𝑎 𝑥 − ℎ + 𝑘
A.
𝑦 = 𝑎(𝑥 + ℎ)2
−𝑘
C.
𝑦 = 𝑎(𝑥 − ℎ)2+𝑘

7. Which of the following
is the formula for ℎ in
vertex form
𝑦 = 𝑎(𝑥 − ℎ)2
+𝑘
A.
𝑏
𝑎
C.
𝑏
2𝑎
D.
−𝑏
𝑎
B.
−𝑏
2𝑎

8. Which of the following
is the formula for 𝑘 in
vertex form
𝑦 = 𝑎(𝑥 − ℎ)2
+𝑘
A. 𝑐 −
𝑏
2𝑎
C. 𝑐 −
𝑏
4𝑎
B. 𝑐 −
𝑏2
2𝑎
D. 𝑐 −
𝑏2
4𝑎

9. What is the vertex
of the quadratic
function
𝑦 = 𝑥2
+ 6𝑥 + 3?
C. (3,6)
B. (-3,6)
D. (3,-6)
A. (-3,-6)

15. Time (seconds)
𝑥 − 𝑎𝑥𝑖𝑠
y−𝑎𝑥𝑖𝑠
(h,
k) ●

16. A basketball is shot with an initial vertical
velocity of 24 ft/s from 6 feet above the
ground. The ball’s height ℎ in feet is
modeled by ℎ 𝑡 = −16𝑡2 + 24𝑡 + 6
where 𝑡 is the time in seconds after the
ball is shot. What is the maximum height
of the ball and when does the ball will
reach this height?
●𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝑝𝑜𝑖𝑛𝑡
or Vertex
(h,k)

17. A toy rocket is launched from the top of a 30m
high building so that its height , h in meters
above the ground in t seconds later is given by
ℎ 𝑡 = 30 + 64𝑡 − 16𝑡2
. What is the maximum
height attained by the toy rocket? When does
the toy rocket reach its maximum height?

18. Fifteen years from now, perhaps,
you could somehow reach the
maximum height of your
achievement. When that time
comes, what personality and
attitude you should possess/have?

19. Evaluation:
A cannonball is fired and its height,
h, in meters, above the ground, t
seconds after being fired, is given by
ℎ 𝑡 = −5𝑡2
+ 40𝑡 + 3 . What is
the maximum height attained by the
cannonball? How long will it reach
the maximum height?

20. Assignment:
From a 96-foot building, an object is thrown
straight up into the air then follows a
trajectory. The height H(t) of the ball above the
building after t seconds is given by the
function ℎ 𝑡 = 80𝑡 − 16𝑡2 .
1. What maximum height will the object
reach?
2. How long will it take the object to reach the
max. height?
Watch this in youtube:
https://www.youtube.com/watch?v
=qSgwSfa4q08

21. Video Watching:
Watch this in youtube:
https://www.youtube.com/watch?v
=qSgwSfa4q08