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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:


Unique Information:

• y-‐intercept ( 0 , c )

Tells us:


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


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


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]


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


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


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


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]


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]


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]

120

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