Vertex Questions
1. Find the vertex for each of the following equations. State if it is a minimum or a maximum.
(a) y  x 2  2 x  8
(b) y  3x 2  6 x  9
(c) y  5  12 x  x 2
2. A baseball is thrown from the outfield to home plate. The height, h, in meters, of the ball at time, t, in
seconds, is given by h(t )  1.5  14.7t  4.9t 2 .
(a) What is the initial height of the ball?
(b) What is the maximum height reached by the ball?
(c) After how many seconds is the maximum height reached?
3. At an airshow, a plane is performing a power dive. The path of a power dive is given by the equation
h  t 2  10t  80 , where h is the height of the plane in meters and t is the time in seconds.
(a) What was the minimum height of the plane?
(b) At what height did the plane start the power dive?
4. In a game of volleyball, a player serves the ball so that the height of its trajectory h, in meters, after the
time in flight t, in seconds, is given by h  2  9.8t  4.9t 2 .
(a) What is the initial height of the volleyball?
(b) Find the maximum height reached by the ball.
(c) Is the ball high enough to go over a 3.5 m net if it takes 0.5 s to reach the net?
5. A house lot is rectangular with one side bordering on the street. Not including the street side, the
remaining three sides are allowed to have a total length of 120 m. What dimensions will ensure a
maximum area for the lot?
6. Page 34 #26a,c, 27, 29
7. The difference between two numbers is 16. Twice the square of the larger minus six times the smaller
is to have a minimum value. Find the minimum value.
8. A fence is to be built around an area such as the one shown below. What must be the values of x and y
if the area is to be a minimum and the perimeter is to be 300m?
x
x
x
y
y
4y
9. Leo the Lion was bragging about how he could throw a coconut and hit a target 20 m away. Halfway
between him and the target was a banana tree (not quite 5 m high) and 6 m beyond this was a 3.5 m tall
fence. If the coconut just missed the tree Leo claimed it would also clear the fence. Was Leo lyin’?