Chapter 6 Review
Textbook
10 Math Workbook
Chapter
Chapter 6
Section
Chapter 6 Review
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

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

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

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

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

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

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

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

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

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

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

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}

Q3d

Solve by factoring.

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

Q4a

Solve by factoring.

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

Q4b

Solve by factoring.

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

Q4c

Solve by factoring.

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

Q4d

Solve by factoring.

\displaystyle k^{2}-36=0

Q4e

Solve by factoring.

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

Q4f

Solve.

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

Q5a

Solve.

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

Q5b

Solve.

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

Q5c

Solve.

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

Q5d

Solve.

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

Q5e

Solve.

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

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.

Q6

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

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

Q7a

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

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

Q7b

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

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

Q7c

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

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

Q7d

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

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

Find the \displaystyle x  -intercepts and the vertex of each parabola. Then, sketch its graph.
\displaystyle y=x^{2}-16