Chapter 6 Review
Textbook
10 Math Workbook
Chapter
Chapter 6
Section
Chapter 6 Review
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Solutions 31 Videos

Rewrite each relation in the form \displaystyle y=a(x-h)^{2}+k by completing the square. Use algebra tiles or a diagram to support your solution.

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

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Q1a

Rewrite each relation in the form \displaystyle y=a(x-h)^{2}+k by completing the square. Use algebra tiles or a diagram to support your solution.

\displaystyle y=x^{2}+4 x+5

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Q1b

Rewrite each relation in the form \displaystyle y=a(x-h)^{2}+k by completing the square. Use algebra tiles or a diagram to support your solution.

\displaystyle y=x^{2}+10 x+18

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Q1c

Rewrite each relation in the form \displaystyle y=a(x-h)^{2}+k by completing the square. Use algebra tiles or a diagram to support your solution.

\displaystyle y=x^{2}+12 x+26

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Q1d

Find the vertex of each parabola. Sketch the graph, labelling the vertex, the axis of symmetry, and two other points.

\displaystyle y=x^{2}+10 x+15

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Q2a

Find the vertex of each parabola. Sketch the graph, labelling the vertex, the axis of symmetry, and two other points.

\displaystyle y=x^{2}-8 x+4

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Q2b

Find the vertex of each parabola. Sketch the graph, labelling the vertex, the axis of symmetry, and two other points.

\displaystyle y=-x^{2}+6 x-4

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Q2c

Find the vertex of each parabola. Sketch the graph, labelling the vertex, the axis of symmetry, and two other points.

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

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Q2d

Use a graphing calculator to find the maximum or minimum point of each parabola rounded to the nearest tenth.

\displaystyle y=2.7 x^{2}+1.2 x+1.5

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Q3a

Use a graphing calculator to find the maximum or minimum point of each parabola rounded to the nearest tenth.

\displaystyle y=-1.1 x^{2}-0.8 x+1.3

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Q3b

Use a graphing calculator to find the maximum or minimum point of each parabola rounded to the nearest tenth.

\displaystyle y=3.1 x^{2}+5.2 x-2.3

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Q3c

Use a graphing calculator to find the maximum or minimum point of each parabola rounded to the nearest tenth.

\displaystyle y=-\frac{1}{2} x^{2}-\frac{2}{3} x+\frac{3}{4}

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Q3d

Solve by factoring.

\displaystyle x^{2}+11 x+24=0

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Q4a

Solve by factoring.

\displaystyle y^{2}+5 y-36=0

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Q4b

Solve by factoring.

\displaystyle u^{2}-7 u+6=0

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Q4c

Solve by factoring.

\displaystyle q^{2}-16 q+64=0

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Q4d

Solve by factoring.

\displaystyle k^{2}-36=0

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Q4e

Solve by factoring.

\displaystyle 2 m^{2}-m-21=0

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Q4f

Solve.

\displaystyle y^{2}=7 y-12

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Q5a

Solve.

\displaystyle a^{2}+10 a=-24

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Q5b

Solve.

\displaystyle 8 m^{2}=3-2 m

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Q5c

Solve.

\displaystyle 6 p^{2}+20=23 p

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Q5d

Solve.

\displaystyle 8 r^{2}=2 r+21

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Q5e

Solve.

\displaystyle 2 x^{2}-x=6

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Q5f

The length of the hypotenuse of a right triangle is 3 cm more than twice that of the shorter leg. The length of the longer leg is 2 cm more than twice that of the shorter leg. Find the lengths of the three sides of the triangle.

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Q6

Find the \displaystyle x -intercepts and the vertex of each parabola. Then, sketch its graph.

\displaystyle y=x^{2}+12 x+32

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Q7a

Find the \displaystyle x -intercepts and the vertex of each parabola. Then, sketch its graph.

\displaystyle y=x^{2}-8 x+12

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Q7b

Find the \displaystyle x -intercepts and the vertex of each parabola. Then, sketch its graph.

\displaystyle y=-x^{2}+2 x+15

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Q7c

Find the \displaystyle x -intercepts and the vertex of each parabola. Then, sketch its graph.

\displaystyle y=-x^{2}+8 x-7

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Q7d

Find the \displaystyle x -intercepts and the vertex of each parabola. Then, sketch its graph.

\displaystyle y=x^{2}+6 x

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Q7e

Find the \displaystyle x -intercepts and the vertex of each parabola. Then, sketch its graph.

\displaystyle y=x^{2}-16

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Q7f