1. A quadratic function has zeros at (1, 0) and (-3, 0) and passes through the point (2, 10). Write

the equation in vertex form.

2. Is it possible to solve x³+4x²-2x=0 using the quadratic formula? If so, solve it. If not, explain why.

3. Use the descriminant to determine the number of real solutions of the following quadratic

equations and state how you know. (You do not need to solve).

a) -3x²-4x+8=0

b) 5x²+2x+1=0

4.The population growth and decline of a small city is modelled by the quadratic function P(t)=-0.5(t-14)²+72,where P(t) is the population in thousands and t is the time in years since 1990. According to this model:

a) In what year is the population expected to reach a maximum?

b) What is the maximum population?

c) What is the expected population in 2011?

d) In what year(s) is the population expected to be 54,000?

5 The daily profit, P(x), of an amusement park is modelled by P(x)=-25x²+950x+8000, where x is the cost of a ticket in dollars. According to the model,

a) How much should the park charge per ticket to make a maximum profit?

b) What is the maximum daily profit?