Determining Equation of a Quadratic Function

1.     Determine the equation of a parabola in standard form with roots at x = -3 and x = 4, that passes through the point (1,60).

ANSWER:  y = -5x^2 + 5x + 60                    Video Solution

2.     Determine the equation of a parabola in standard form with a vertex at (-3, 5) and that passes through the point (-5, 37)

ANSWER:  y = 8x^2 + 48x + 77                    Video Solution

Word Problem

3.     A tunnel with a parabolic arch is 8m wide.  If the height of the arch 1 metre from the outer edge is 3 metres, can a truck that is 6 metres tall and 3 metres wide fit through the tunnel?

Word Problems:  Maximum and Minimum

Trajectory

4.     A toy rocket is launched off the roof of a building.  Its height h in metres at time t in seconds is given by the function h(t) = -4.9t^2 + 34.3t + 39.2

a)   How high is the roof?

b)   When will the rocket hit the ground?

c)   When does the rocket pass at roof level on the way down?

d)   When does the rocket achieve its maximum height?

e)   What is the maximum height?

f)   For how long is the rocket above 88.2 m?

ANSWERS:  a)  39.2 m        b)  8 seconds        c)  7 seconds        d)  3.5 seconds        e)  99.2 m        f)  3 seconds                    Video Solution

Revenue

5.     Felix owns a business selling exotic snowglobes.  He knows that if he sells them for \$30 each, he can sell a total of 1600 snowglobes.  However, for every one dollar increase in price, he sells 20 fewer snow globes.

a)     What price should he charge per snow globe to maximize his revenue?

b)     What is the maximum possible revenue?

ANSWERS:    a)  \$55          b)  \$60 500                    Video solution

Maximum Area (e.g., Fence around a Garden, Max. Sunlight)

6.     Mohammed has 20 m of fence as shown.  He wishes to put fencing around the outside of his garden.  He plans to build it against his house so that there is no need for fencing to be put along that side.

a)     What are the dimensions of the largest garden possible (maximum area)?

b)     What is the area of the largest possible garden?

ANSWERS:  a)  5 m by 10 m        b)  50 m^2                   Video Solution 7.     Fatima has 72 m of fence as shown.  She wishes to put fencing around the outside of her garden.  She plans to build it against her house so there is no need for fencing to be put along that side.

a)     What is the largest possible total area?

b)  What are the possible dimensions if Fatima want each of the three pens to be 96 m^2 in area?

ANSWERS:     a)  324 m^2        b)  either each of the four identical sides is 6 m and the long side is 48 m, or each of the four identical sides is 12 m and the long side is 24 m.                    Video Solution to 8.     Hemza has 60 metres of fence with which to build the rectangular garden shown.  He plans to build it aginst his house so there is no need for fencing to be placed along that side.  What is the maximum possible area that can be enclosed? Word Problems:  Finding Zeros

Border Questions

9.     Border Outside the Established Rectangle:  Sarah has a rectangular photo that is 30 cm X 40 cm.  She want to build a frame of uniform width around the outside of it and she can afford 624 cm^2 of wood for the frame.  How wide will the frame be?

10.     Border Inside the Established Rectangle:     Zheng's lawn is a rectangle measuring 20 m by 12 m.  He wants to dig up some of his lawn in order to make a sidewalk of uniform width all around.  How wide will the walkway be, given that he can afford 60 m^2 of cement?

Mixed Questions

11.     A rectangle has one side 5 cm longer than the other.  The total area is 176 cm^2.  What are the dimensions of the rectangle?

ANSWER:     16 cm X 11 cm                      Video Solution

12.     The sum of the squares of two consecutive integers is 925.  What are the integers?

ANSWER:     Either 21 and 22    or    -22 and -21                  Video Solution

13.     The sum of the squares of three consecutive odd positive integers is 875.  What are the integers?

ANSWER:     15, 17 and 19                   Video Solution

14.     A right angled triangle has a perimeter of 120 cm.  The hypotenuse is 6 m longer than one of the sides.  How long are the sides?

ANSWER:     24 cm, 45 cm and 51 cm.        Video Solution