MCF3Ml

Unit 3 Test: Quadratic Functions Narne _67

/19 /8 /30 /10

PART A - KNOWLEDGE AND UNDERSTANDING ---- MARKS19

MatchingMatch the formula with its name.

Name FormulaJExample

_____ Discriminant

_____ Quadratic Formula

___ Quadratic Expression c. (x - 2)

___ Quadratic Function D. D = b2 -4ac

____ Quadratic Equation E. x = 2

____ An example of a factor F. x =( -b ± ..J b2 -4ac )/2a

___ An example of a root G. ax2+ bx + c

7

- Page 2-

TrueIFalseIndicate whether the statement is true or false.

1. The value k = 12 makes the expression x2 +kx+ 36 a perfectsquare trinomial.

2. The exact roots of X2 + 2x- 15 = 0 are 5 and -3.

3. To the nearest hundredth, the x-intercepts of y = -2x2 + 3x- 3 are-0.69 and 2.19.

4. The equation of a parabola whose graph passes through points(3,0) and (-4, 0) and has a minimum at (-0.50, -12.25) is

2y=x +x-12.

Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

5. The value of k that makes the expression x2 + 8x + k a perfect square trinomial is

a.b.

1632

c.d.

-32121

6. The vertex form of y = x2 - 6x+ 13 is

a.b.

Y= (x+ 3i + 4Y= (x-3)2+4

c.d.

y = (x- 4i + 3y = (x+ 4)2 - 3

7. Find the minimum value of y = 2x2 + 12x + 17 by completing the square.

a.b.

-1-3

c.d.

117

- Page 3-

8. The x-intercepts, to the nearest hundredth, of y = 4x2 + 5x - 6 are

a.b.

-0.75 and -2.00-2.00 and 0.75

c.d.

0.75 and 2.00non-existent

9. The number of real roots the equation y = X2 - 8x + 4 has is

a. o b. 1 c. 2

10. The number of real roots the equation y = -3x2 + 4x- 5 has is

a. o b. 1 c. 2

11. Which choice best describes the graph of y = X2 + X - 6?

y

8 "I

a. • positive for x > -3 and x < 2• negative for -3 < x < 2• increasing for x> -0.5• decreasing for x < -0.5

c. • positive for x < -3 and x > 2• negative for x > 2• increasing for x < -0.5• decreasing for x > -0.5

b. • positive for x < -3 and x> 2• negative for -3 < x < 2• increasing for x> -0.5• decreasing for x < -0.5

d. • positive for x> -3 and x < 2• negative for -3 < x < 2• increasing for x > -0.5• decreasing for x > -0.5

-Page4-

12. The table shows the curve of a parabolic arch at the entrance to a park,where x is the horizontal distance from one side of the arch and h is the height ofthe arch above ground, both in metres.

x h1 12 43 54 45 1

The coordinates of the vertex arc

a.b.

(3,3)(2,4)

c.d.

(5, 3)(3,5)

PART B - COMMUNICATION -MARKS8

Complete each statement.

13. Completing the square is the process of rewriting a quadratic function fromthe form to the vertex form.

14. Completing the square can be used to find the value ifthe quadratic function opens down.

15. In order to solve a quadratic equation, the equation first must equal

16. The number of x-intercepts of a quadratic equation ax2 + bx « c = 0 canquickly be determined using the _

17. If the discriminant of a quadratic equation is equal to a perfect square, thenthe equation can be _

- Page 5-

18. If the discriminant of a quadratic equation is less than 0, then the equationhas real root(s).

19. For a quadratic function, increasing and decreasing regions are horizontallyseparated by the _

20. In order to write a quadratic equation, in factored form, the_________ are used from the parabolic graph.

PART C - APPLICATION --MARKS26

Short Answer (show your work)

21. Determine the number of real roots for the equation 3x2 = 8x - 4. Then, find the rootsof the equation by factoring.

7

- Page 6-

22. Find the x-intercepts of the quadratic function y = 3x2- lOx + 6. Round your answer- ~

to the nearest hundredth, if necessary.

5

23. Write an equation in standard form for this parabola.

(15, -1'2.25),

<Page 7-............................................................................................................................................................... " - .

24. The quadratic function y = X2 - 5x - 14 can be factored.

a) Find the x-intercepts.

b) Find the y- intercept.

c) Find the coordinates of the vertex.

d) Find the equation of the axis of symmetry.

e) Determine the intervals for which the function is:

A. Positive

B. Negative

C. Increasing

D. Decreasing

3

1

4

1

4

- Page 8-

PART D - INQUIRY 10 MARKS

25. When Jamie skis off a ramp, his path can be modelled by h(d) = -4.9d2 + 4.7d + 2.5,where d is the horizontal distance from the ramp and h(d) is his height, both in metres.

a) How high off the ground is the ramp?

b) How far away from the end of the ramp does he land, to the nearest tenth of a metre?

c) What is Jamie's maximum height?

1

4

5