Finding the Zeros in Vertex Form Worksheet
1. a) Determine the y-intercept.
b) Find the zeros.
i) y = -(x + 5)2 + 1
iv) y = ½(x + 7)2 – 18

ii) y = -3(x + 3)2 + 75
v) y = -⅓(x – 2)2 + 12
iii) y = 2(x – 1)2 – 8
vi) y = ¼(x – 8)2 – 25
2. A concert promoter models the profit from her next concert, P dollars, by the equation
2
P  11t  55  10571, where t dollars is the cost per ticket.
a) What price should she charge to maximize her profit? What is the maximum profit?
b) What will be her profit if the tickets were free?
c) How much should she charge per ticket to break-even?
3.
A flare is released into the air following the path, h  5(t  6) 2 182, where h is the height in
meters and t is the time in seconds.
a) What was the flare’s maximum height?
b) What was the flare’s initial height? 
c) How long was the flare in the air?
4. On a sunny day, the daily profit, P dollars, of a popcorn vendor is modelled by the equation
P = -60(x – 4)2 + 120, where x is the price of a bag of popcorn.
a) What should the price be to maximize the daily profit? What is the maximum daily profit?
b) Determine the price needed for the vendor to break-even.
5. Teresa heads the ball in soccer. The path of the ball is described by the equation
h = -0.2(d – 2)2 + 2.8, where h metres is the height of the ball and d metres is its distance
measured horizontally from where Teresa hits it.
a) Determine the initial height of the ball.
b) Determine the maximum height of the ball.
c) Determine how far the ball travels.
6. The h height, in metres, of a football can be modeled by the equation, h = -5(t – 2)2 + 20 after t
seconds.
a) How long did it take for the ball to reach it’s maximum height? What was the ball’s maximum
height?
b) When will the ball hit the ground?
Answers
1. i) a) (0, -24) b) (-4, 0), (-6, 0) ii) a) (0, 48) b) (-8, 0), (2, 0) iii) a) (0, -6) b) (-1, 0), (3, 0) iv) a) (0, 13/2) b) (-13, 0), (-1, 0) v) a) (0, 32/3)
b) (-4, 0), (8, 0) vi) a) (0, -9) b) (-2, 0), (18, 0) 2. a) $10571, $55 b) -$22704 c) $24, $86 3. a) 182 m b) 2 m c) 12.03 s 4. a) $4, $120
b) $2.59, $5.41 5. a) 2 m b) 2.8 m c) 5.74 m 6. a) 2s, 20 m b) 4 s