QUADRATICS
MAKE SENSE
Word Problems
Tips/Hints
What was the initial height?
-> set x=0 and solve for y [find the y intercept]
How long was "the ball" in the air?
-> set y=0 and solve for x [find the x intercepts]
-> 'the time when the ball hit the ground' is the same
What is the maximum height of "the ball"?
-> the y value of the vertex
What time did the ball reach its maximum height?
-> the x value of the vertex
What is the heght of the ball at 5 seconds?
-> sub 5 into the equation and solve for y
Example 1
The height of a ball, h metres, t seconds after it is thrown can be shown using the equation h = -5 (t - 3)^2 + 46.5
a) What was the maximum height of the ball?
The vertex of the equation is (3,46.5). Therefore, the max height of the ball is 46.5m because that is the y value of the vertex.
b) How long does it take the ball to reach its maximum height?
It took the ball 3 seconds to reach its max height because that is the x value of the vertex.
c) What was the height of the ball after it was thrown?
Therefore the initial height is 1.5m
d) What was the height of the ball after 2 seconds?
Therefore the height of the ball after 2 seconds is 41.5m
Example 2
On a sunny day, the daily profit, P dollars, of an ice cream truck is shown by the equation P = -60 (x - 4)^2 + 120, where x is the price of the ice cream.
a) What should the price be to maximize the daily profit? What is the maximum daily profit?
The price to maximize daily profit should be $4 because that is the x value of the vertex. The max daily profit is $120, because that is the y value of the vertex.
b) Determine the price needed for the vendor to break even? (profit = 0)
Therefore the prices that would make the
profit = $0 would be $5.41 and $2.50
