Unit 3 quadratic functions test for mathematics calculus

Which of the following is true about the parabola for the function?. Which of the following are roots of the equation.. What is the value of the discriminant for the function?. b Graph t

Unit 3 Test: Quadratic Functions Name: K= /16 A= /17 C= /3 T= /4

Total /40

Part A: Multiple Choice (circle the best answer for each question) [K=5]

1 Which of the following is true about the parabola for the function ?

a The y-intercept is 0. c The axis of symmetry is x = – 4.

b The vertex is (4, 5) d The parabola opens down

a They have the same y-intercept c They have the same x-intercepts.

b They have the same vertex d They have the same axis of symmetry

3 Which of the following quadratic functions will have a minimum value?

4 Which of the following are roots of the equation ?

5 What is the value of the discriminant for the function ?

Input your answers here for the above multiple choice questions.

Part B: Short answers Show steps for full marks.

6 (a) Given a function y   3 x2  12 x  8 , rewrite the function in vertex form by

6 (b) Graph the function and indicate the vertex and two other points on the graph

Label the graph properly

[K=3]

7 Determine the roots of the equation by factoring Explain how you

8 Use the quadratic formula to determine each of the roots of – 7x2 – 23x + 10 = 0 to two

9 Determine algebraically the coordinates of the point(s) of intersection of the system

10 Write the equation of the quadratic function given the x-intercepts are 5 and 1  , and

[A=4]

11 Find the value(s) of k so that the graph of the function f x  2 x2  kx  50 has one

12 The cost function for a telephone manufacturing plant is C(x) = 4x + 169 and the revenue function is R(x) = –2x2 + 48x, where x is the number of telephones sold, in thousands

a) Determine the profit function for the number of phones sold [A=5] b) Determine the number of telephones sold that maximizes profit

c) Determine the maximum profit in thousands

13 A model rocket is launched off the top of a table The height of the rocket is given by the

function, h(t) = - 4.9t2 + 9.5t + 1.2 where h(t) is the height in metres and t is the time in seconds

How long will it take for the rocket to reach the ground? Answer in 2 decimal places [T=4]