Vertex Form: y = a(xh) 2 +k Factored Form: y = a(xr)(xs) Chapter 4 Practice Test Section 1: Multiple Choice - circle the correct response (4 marks) 1. Use finite differences to determine the type of relation between x and y. x y 5 –7 4 0 3 3 2 0 1 7 a. linear c. neither linear nor quadratic b. quadratic d. unable to determine 2. Use finite differences to determine the type of relation between x and y. x y –3 20 –2 10 –1 4 0 2 1 4 a. linear c. neither linear nor quadratic b. quadratic d. unable to determine 53
Transcript
Vertex Form: y = a(x-‐h)2 + k Factored Form: y = a(x-‐r)(x-‐s)
Chapter 4 Practice Test Section 1: Multiple Choice - circle the correct response (4 marks)
1. Use finite differences to determine the type of relation between x and y. x y 5 –7 4 0 3 3 2 0 1 7
a. linear c. neither linear nor quadratic
b. quadratic d. unable to determine
2. Use finite differences to determine the type of relation between x and y. x y
–3 20 –2 10 –1 4 0 2 1 4
a. linear c. neither linear nor quadratic b. quadratic d. unable to determine
53
Vertex Form: y = a(x-‐h)2 + k Factored Form: y = a(x-‐r)(x-‐s)
3. Which one of the following graphs best represents the equation y=x2+3?
a. c.
b. d.
4. Which one of the following graphs represents the equation y=-2(x+1)2+1 ?
a. c.
b. d.
Vertex Form: y = a(x-‐h)2 + k Factored Form: y = a(x-‐r)(x-‐s)
Section 2: Vertex Form (24 marks)
5. Complete the chart for each quadratic relation [3 marks each] a) b)
6. Describe the transformations from y=x2 to y= -‐2x2 -‐ 9 [3 marks]
7. Write an equation, in the form y = a(x-‐h)2 + k , for the parabola with vertex at (-‐4,5), opening upward, and with a vertical stretch of factor 7 [3 marks]
Property 𝒚 =𝟏𝟐 𝒙+ 𝟏 𝟐
vertex
axis of symmetry
stretch or compression and by what factor?
direction of opening
values that x may take
values that y may take
Property y = -‐3(x − 5)2 + 7
vertex
axis of symmetry
stretch or compression and by what factor?
direction of opening
values that x may take
values that y may take
Vertex Form: y = a(x-‐h)2 + k Factored Form: y = a(x-‐r)(x-‐s)
8. Determine an equation, in the form y = a(x-‐h)2 + k , for the following parabola: [4 marks]
Equation of the parabola is: _____________________________________
9. The graph of y=x2 is stretched vertically by a factor of 2, reflected in the x-‐axis, and then translated 2 units up and 1 unit right. [8 marks]
a) Equation of the parabola:
b) Vertex:
c) Axis of symmetry:
Vertex:
Second Point: (1,1)
Vertex Form: y = a(x-‐h)2 + k Factored Form: y = a(x-‐r)(x-‐s)
d) Graph the parabola using a table of values. LABEL THE VERTEX.
Section 3: Factored Form (15 marks)
10. State the x-‐intercepts of the following [3 marks]: a) y = 4(x+5)(x+3)
b) y = 55(x-‐1)(x-‐7)
c) y= ½x(x-‐3)
x
y
Vertex Form: y = a(x-‐h)2 + k Factored Form: y = a(x-‐r)(x-‐s)
11. For the quadratic relation y = 2(x+4)(x-‐2) : [8 marks]
a. What are the x-‐intercepts?
b. What is the axis of symmetry?
c. What is the vertex?
d. Sketch the graph (label the vertex and x-‐intercepts)
Vertex Form: y = a(x-‐h)2 + k Factored Form: y = a(x-‐r)(x-‐s)
12. Determine the equation, in the form , for the parabola shown. [5 marks]
x – intercepts:
second point: (0,-4)
Equation of the parabola is: _____________________________________
Section 4: Applications (10 marks)
13. The path of a rocket is given by the relation 𝒉 = −𝟎.𝟎𝟔𝟐𝟓𝒅(𝒅− 𝟓𝟔), where d represents the horizontal distance, in metres, the rocket travels and h represents the height, in metres, above the ground of the rocket at this horizontal distance. [5 marks]
a) At what horizontal distance does the rocket reach its maximum height?
Vertex Form: y = a(x-‐h)2 + k Factored Form: y = a(x-‐r)(x-‐s)
b) What is the maximum height of the rocket? c) At what horizontal distance does the rocket hit the ground?
14. Mr. Jensen was shot out of a cannon. His flight is represented by the equation h = -‐ 4.9(t -‐ 6)2 + 182, where h is the height, in metres, above the ground and t is the time, in seconds. [5 marks]
a) Find the maximum height of Mr. Jensen. b) How long does it take him to reach the maximum height? c) How high was he above the ground when he was launched out of the cannon? Bonus: What are the x-intercepts of the parabola y=-15(2x-4)(-6x+1)
Vertex Form: y = a(x-‐h)2 + k Factored Form: y = a(x-‐r)(x-‐s)
Answers:
1) C 2) B 3) C 4) A 5) a) Vertex (5,7) ; aos is x=5 ; stretch vertically by a factor of 3, opens down, x can be any real number, y
is less than or equal to 7. b) Vertex is (-‐1, 0), aos is x=-‐1, compressed vertically by a factor of ½, opens up, x can be any real number, y is greater than or equal to 0.
6) Reflect in the x-‐axis, stretched vertically by a factor of 2, translated 9 units down. 7) 𝑦 = 7(𝑥 + 4)! + 5 8) 𝑦 = − !
!𝑥 + 2 ! + 4
9) a) 𝑦 = −2 𝑥 − 1 ! + 2 b) vertex (1, 2) c) x=1 d)
