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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

`\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

`\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

`\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