Quadratic Application Solutions

Application Question #1 A pole vaulter's height when she leaves the  ground is modelled by the function 

where h(t) is her height in metres and t is  time in seconds that she is in the air.

(a) How long was she in the air, to one decimal place?

(b) How high was she at 0.5 seconds?

(c)  For how long was she above 3 m, to one decimal place?

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Quadratic Application Solutions

Application Question #2 A ball is thrown vertically upward off the roof of a 34‐m tall  building. The height of the ball, h(t) in metres can be  approximated by the function h(t) = ‐5t2  + 10t +34, where t is  the time in second after the ball is thrown. (a)  How high is the ball after 2 seconds? (b)  Find the maximum height of the ball?

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Quadratic Application Solutions

Application Question #3 A Frisbee is passed to another teammate in a game of  Ultimate Frisbee. The Frisbee follows the path                     h(d) = ‐0.02d2 + 0.4d + 1, where h(d) is height in metres and  d is the horizontal distance in metres that the Frisbee  travelled from the thrower.

(a)  What is the maximum height of the Frisbee? (b)  What is the horizontal distance from the thrower at the maximum height? (c)  If the Frisbee is intercepted by a player 17 m down the field, how high will  it be at the moment it is intercepted?

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Quadratic Application Solutions

Application Question #4 A new skateboard half‐pipe is being built. The diagram shows the cross‐ section where x represents the horizontal distance from the platform, in  metres, and y represents the height above the ground, in metres. Determine  the equation that models the half‐pipe shape. Express the equation in  standard form.

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Quadratic Application Solutions

Application Question #5 An open‐topped box is to be made from a piece of tin measuring 50 cm by 30  cm.  The sides of the box are formed when four congruent square corner  pieces are cut out.  The base area of the box is to be 1269 cm2. 30 cm

50 cm

(a)  Determine an equation for the base area of the box. (b)  Find the side length, x, of the square cut from each corner. (c)  Find the dimensions of the box.

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Quadratic Application Solutions

Application Question #6 Amir sells his extreme cheesesteak sandwiches for $8 each.  At this price, he  usually sells 100 cheesesteak sandwiches a day.  Amir is considering raising  the price.  After an informal survey, he concludes that for every $0.50  increase, he will sell five fewer sandwiches.  What price should Amir charge to maximize his revenue?  What is the maximum revenue?

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6

Lesson 7 Application Solutions.pdf

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