Mid Chapter Review
Chapter
Chapter 6
Section
Mid Chapter Review
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Solutions 33 Videos

Solve the quadratic equation.

\displaystyle x^2 + 4x = 12

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0.31mins
Q1a

Solve the quadratic equation.

\displaystyle x^2 + 8x + 9 = 0

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0.51mins
Q1b

Solve the quadratic equation.

\displaystyle x^2 -9x = -4

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1.10mins
Q1c

Solve the quadratic equation.

\displaystyle -3x^2 -2x + 3 = 0

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1.26mins
Q1d

Solve the quadratic equation.

\displaystyle 2x^2 - 5x + 10 = 15

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1.29mins
Q1e

Solve the quadratic equation.

\frac{1}{2}x^2 + 10x - 2 = -10

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1.12mins
Q1f

Determine the root(s).

\displaystyle x^2 + 6x - 16 = 0

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0.26mins
Q2a

Determine the root(s).

\displaystyle 2x^2 + x - 3= 0

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1.12mins
Q2b

Determine the root(s).

\displaystyle x^2 + 3x - 10 = 0

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0.21mins
Q2c

Determine the root(s).

\displaystyle 6x^2 + 7x - 5 = 0

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0.56mins
Q2d

Determine the root(s).

\displaystyle -3x^2 -9x + 12 = 0

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0.39mins
Q2e

Determine the root(s).

\displaystyle \frac{1}{2}^2 + 6x + 16 = 0

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0.33mins
Q2f

Solve using any strategy.

\displaystyle x^2 + 12x + 45 = 0

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0.25mins
Q3a

Solve using any strategy.

\displaystyle 2x^2 + 7x + 5 = 9

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0.40mins
Q3b

Solve using any strategy.

\displaystyle x(6x -1) = 12

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0.56mins
Q3c

Solve using any strategy.

\displaystyle x(x + 3) - 20 = 5(x + 3)

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0.47mins
Q3d

Kate drew this sketch of a small suspension bridge over a gorge near her home.

She determined that the bridge can be modelled by the relation y = 0.1x^2 - 1.2x + 2. How wide is the gorge, if 1 unit on her graph represents 1 m?

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1.43mins
Q4

If a ball were thrown on Mars, its height, h, in metres, might be modelled by the relation h = -1.9t^2 + 18t + 1, where tis the time in seconds since the ball was thrown.

a.Determine when the ball would be 20 m or higher above Mars’ surface.

b. Determine when the ball would hit the surface.

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5.17mins
Q5

Determine the value of c needed to create a perfect-square trinomial.

\displaystyle x^2 + 8x + c

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0.12mins
Q6a

Determine the value of c needed to create a perfect-square trinomial.

\displaystyle x^2 - 10x + c

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0.10mins
Q6b

Determine the value of c needed to create a perfect-square trinomial.

\displaystyle x^2 + 5x + c

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0.12mins
Q6c

Determine the value of c needed to create a perfect-square trinomial.

\displaystyle x^2 - 7x + c

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0.13mins
Q6d

Determine the value of c needed to create a perfect-square trinomial.

\displaystyle -4x^2 + 24x + c

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0.30mins
Q6e

Determine the value of c needed to create a perfect-square trinomial.

\displaystyle 2x^2 -18x + c

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0.40mins
Q6f

Write each relation in vertex form by completing the square.

\displaystyle y = x^2 + 6x -3

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0.28mins
Q7a

Write each relation in vertex form by completing the square.

\displaystyle y = x^2 -4x + 5

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0.24mins
Q7b

Write each relation in vertex form by completing the square.

\displaystyle y = 2x^2 + 16x + 30

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0.42mins
Q7c

Write each relation in vertex form by completing the square.

\displaystyle y = -3x^2 -18x - 17

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0.44mins
Q7d

Write each relation in vertex form by completing the square.

\displaystyle y = 2x^2 + 10x + 8

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1.09mins
Q7e

Write each relation in vertex form by completing the square.

\displaystyle y = -3x^2 + 9x -2

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1.06mins
Q7f

Consider the relation y = -4x^2 + 40x - 91.

a. Complete the square to write the equation in vertex form.

b. Determine the vertex and the equation of the axis of symmetry.

c. Graph the relation.

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2.01mins
Q8

Martha bakes and sells her own organic dog treats for \$15/kg. For every \$1 price increase, she will lose sales. Her revenue, R, in dollars, can be modelled by y = -10x^2 + 100x + 3750, where x is the number of \$1 increases. What selling price will maximize her revenue?

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1.39mins
Q9

For his costume party, Byron hung a spider from a spring that was attached to the ceiling at one end. Fern hit the spider so that it began to bounce up and down. The height of the spider above the ground, b, in centimetres, during one bounce can be modelled by h = 10h^2 -40t+240, where t seconds is the time since the spider was hit. When was the spider closest to the ground during this bounce?

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1.19mins
Q10