Chapter Test
Chapter
Chapter 6
Section
Chapter Test
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Solutions 17 Videos

Use the graph of y = 3x^2 + 6x - 7 at the right to estimate the solutions to each equation.

3x^2 + 6x - 7 = 0

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Q1a

Use the graph of y = 3x^2 + 6x - 7 at the right to estimate the solutions to each equation.

3x^2 + 6x - 7 = -7

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Q1b

Use the graph of y = 3x^2 + 6x - 7 at the right to estimate the solutions to each equation.

3x^2 + 6x - 9 = 0

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Q1c

Determine the roots .

\displaystyle x^2 + 5x - 14 = 0

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Q2a

Determine the roots .

\displaystyle 5x^2 - 9x + 1 = 0

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Q2b

Determine the roots .

\displaystyle 2x^2 - 8 = 24

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Q2c

Determine the roots .

\displaystyle 2(x -1)^2 - 5 = 0

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Q2d

Complete the square to find the vertex.

\displaystyle y = 2x^2 + 12x -14

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0.55mins
Q3a

Complete the square to find the vertex.

\displaystyle y = 3x^2 - 15x -24

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1.31mins
Q3b

Can all quadratic relations be written in vertex form by completing the square? Justify your answer.

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Q4

Without solving, determine the number of real roots it has.

y = 2x^2 -4x + 7

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Q5a

Without solving, determine the number of real roots it has.

y =3(x-4)(x-4)

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Q5b

Without solving, determine the number of real roots it has.

y = (x-3)^2

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Q5c

April sells specialty teddy bears at various summer festivals. Her profit for a week, P, in dollars, can be modelled by P = -0.1n^2 + 30n - 1200, where n is the number of teddy bears she sells during the week.

a) According to this model, could April earn a profit of in one week? Explain.

b) How many teddy bears would she have to sell to break even?

c) How many teddy bears would she have to sell to earn $500?

d) How many teddy bears would she have to sell to maximize her profit?

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Q6

Sean and Farah have 24 m of fencing to enclose a vegetable garden at the back of their house. Determine the dimensions of the largest rectangular garden they could enclose, using the back of their house as one of the sides of the rectangle.

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Q7

Give two reasons why 3x^2 + 6x + 6 cannot be a perfect square.

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Q8

A rapid—transit company has 5000 passengers daily, each currently paying a $2.25 fare. For each $0.50 increase, the company estimates that it will lose 150 passengers daily. If the company must be paid at least $15 275 each day to stay in business, what minimum fare must they charge to produce this amount of revenue?

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Q9