MBF3C – FOUNDATIONS OF COLLEGE MATHEMATICS MR. G. PEARSON
MBF3C Culminating Activity Day 2 Name _________________________
QUADRATICS I & II
Vertex Form Standard Form Factored Form y = a(x – h)2 + k y = ax2 + bx + c y = a(x – r)(x – s)
Tells us:
• Direction of opening • Step Pattern
Unique Information:
• Vertex ( h , k )
Tells us:
• Direction of opening • Step Pattern
Unique Information:
• y-‐intercept ( 0 , c )
Tells us:
• Direction of opening • Step Pattern
Unique Information:
• Zeros / Roots ( r , 0 ) , ( s , 0 )
1. Expand and simplify the following expressions. [8 MARKS]
a) 3(2x+ 1) b) −𝑥(𝑥 − 3) c) 2(x− 5)(x+ 3) d) −4(𝑥 − 2)! 2. Factor fully. [8 MARKS]
a) 8𝑥! − 16𝑥! + 12𝑥 b) 𝑥! + 6𝑥 + 8
expanding (FOIL) expanding (FOIL)
factoring trinomials
MBF3C – FOUNDATIONS OF COLLEGE MATHEMATICS MR. G. PEARSON
c) 3𝑥! − 75 d) −3𝑥! − 12𝑥 + 36 3. Solve the following quadratic equations. [11 MARKS]
a) 𝑥! − 3𝑥 − 28 = 0 b) 2𝑥! + 4𝑥 − 30 = 0 c) −5𝑥! − 30𝑥 = 0 d) −2𝑥! + 128 = 0 4. Describe the transformations in each of the following quadratic equations as they compare
to the standard parabola y = x2. [7 MARKS]
a) y = x! + 3 b) y = −0.25(x− 4)! c) y = 3(x+ 2)! − 10
MBF3C – FOUNDATIONS OF COLLEGE MATHEMATICS MR. G. PEARSON
5. Complete the following tables of values and graph each relation. [2 x 6 MARKS]
y = 2x – 3
x y 1st diff. 2nd diff.
-‐3
-‐2
-‐1
0
1
2
3
y = x2 + 4x – 5
x y 1st diff. 2nd diff.
-‐3
-‐2
-‐1
0
1
2
3
6. What do the first and second differences tell us about these equations? Be specific in your
explanation. [2 MARKS]
MBF3C – FOUNDATIONS OF COLLEGE MATHEMATICS MR. G. PEARSON
7. Complete the following table for each parabola. [2 x 10 MARKS]
Parabola A Parabola B
Vertex Vertex
Axis of Symmetry Axis of Symmetry
Direction of Opening Direction of Opening
Min / Max Min / Max
Optimum Value Optimum Value
Zeros Zeros
y-‐intercept y-‐intercept
Step Pattern Step Pattern
Equation Equation
A
B
MBF3C – FOUNDATIONS OF COLLEGE MATHEMATICS MR. G. PEARSON
8. Complete the following table. [8 MARKS]
Equation Vertex Opens Up
/Down
Step Pattern
Axis of Symmetry
Max or Min Value
a) 𝑦 = −(𝑥 + 2)! b) 𝑦 = 2(𝑥 − 1)! + 3 c) -‐3, -‐9, -‐15 𝑥 = 5 max 𝑦 = −4 1 MARK 1.5 MARKS 1.5 MARKS 1 MARK 1 MARK 2 MARKS
9. Graph and label each parabola on the grid below. [6 MARKS]
a) 𝑦 = − 𝑥 − 3 ! + 7 b) 𝑦 = 2(𝑥 + 4)! − 9
MBF3C – FOUNDATIONS OF COLLEGE MATHEMATICS MR. G. PEARSON
10. Match each parabola with the diagram below. Put the correct letter of parabola next to the corresponding equation. [4 MARKS]
𝑦 = 𝑥! − 3 𝑦 = −2𝑥! + 20𝑥 − 48
𝑦 = −3 𝑥 + 5 ! + 12 𝑦 = 0.1(𝑥 + 8)(𝑥 − 6)
A
C
B
D
MBF3C – FOUNDATIONS OF COLLEGE MATHEMATICS MR. G. PEARSON
11. Given the function 𝑦 = −2(𝑥 + 1)! + 32, a) Expand to standard form. [2 MARKS]
b) Factor to factored form and determine the roots. [3 MARKS] 12. Given the function 𝑦 = 3(𝑥 − 2)(𝑥 + 8),
a) Expand to standard form. [2 MARKS]
b) Calculate the axis of symmetry and the coordinates of the vertex. [3 MARKS] 13. Given the function 𝑦 = −𝑥! − 4𝑥 + 21,
a) Factor to factored form. [2 MARKS]
b) Calculate the axis of symmetry and the coordinates of the vertex. [3 MARKS]
MBF3C – FOUNDATIONS OF COLLEGE MATHEMATICS MR. G. PEARSON
14. Cassandra drops a rock off of a bridge into the water below. The path of the rock can be modeled by the equation h = −4.9t! + 60, where h is the height in feet and t is time in seconds.
a) Draw a labeled sketch of this scenario. [1 MARK]
b) How high is the bridge from the surface of the water? [2 MARKS]
c) What was the height of the rock after 3 seconds? [2 MARKS]
d) When will the rock hit the water’s surface? [3 MARKS]
MBF3C – FOUNDATIONS OF COLLEGE MATHEMATICS MR. G. PEARSON
15. Austin hits a golf ball while standing on the same bridge as in the previous question. The path of the ball can be modeled by the equation h = −5t! + 20t+ 60, where h is the height in feet and t is time in seconds. a) Draw a labeled sketch of this scenario. [1 MARK]
b) From what height above the ground is the ball hit? [2 MARKS]
c) What was the height of the ball after 5 seconds? [2 MARKS]
d) What is the maximum height of the ball, and when does this occur? [3 MARKS]
e) When is the ball at a height of 75 feet? [3 MARKS]
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