Chapter

Chapter 6
Section

Chapter Review on Quadratic Equations

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Solutions
39 Videos

Rewrite each relation in the form `y = a(x - h)^2 + k`

by completing the square. Use algebra tiles or a diagram to support your solution.

```
\displaystyle
y =x^2 + 8x -7
```

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Q1a

Rewrite each relation in the form `y = a(x - h)^2 + k`

by completing the square. Use algebra tiles or a diagram to support your solution.

```
\displaystyle
y = x^2 + 2x +7
```

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Q1b

Rewrite each relation in the form `y = a(x - h)^2 + k`

by completing the square. Use algebra tiles or a diagram to support your solution.

```
\displaystyle
y = x^2 + 4x +6
```

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Q1c

`y = a(x - h)^2 + k`

by completing the square. Use algebra tiles or a diagram to support your solution.

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

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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 + 12x + 30
```

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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 - 14x + 50
```

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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 + 6x - 7
```

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Q2c

```
\displaystyle
y = 5x^2 - 40x + 76
```

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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 = 2.1x^2 -2.5x + 8.0
```

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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 = -338x^2+127x -212
```

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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 = \frac{1}{5}x^2 - \frac{2}{25} x + \frac{3}{5}
```

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Q3c

Solve by factoring. Check your solutions.

```
\displaystyle
x^2 + 10x + 21 = 0
```

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Q4a

Solve by factoring. Check your solutions.

```
\displaystyle
m^2 + 8m, - 20 = 0
```

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Q4b

Solve by factoring. Check your solutions.

```
\displaystyle
6y^2 + 21y + 9 = 0
```

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Q4c

Solve by factoring. Check your solutions.

```
\displaystyle
5n^2 + 13n - 6 = 0
```

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Q4d

Solve.

```
\displaystyle
y^2 = 8y + 9
```

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Q5a

Solve.

```
\displaystyle
x^2 - 8x = - 7
```

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Q5b

Solve.

```
\displaystyle
3m^2 = -10m - 7
```

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Q5c

Solve.

```
\displaystyle
30x -25x^2 = 9
```

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Q5d

Solve.

```
\displaystyle
8k^2 = -5 + 14k
```

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Q5e

Solve.

```
\displaystyle
3x^2 + 2 = -5x
```

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Q5f

The length of the hypotenuse of a right triangle is 1 cm more than triple that of the shorter leg. The length of the longer leg is 1 cm less than triple that of the shorter leg. Find the lengths of the three sides of the triangle.

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Q6

Find the x-intercepts and the vertex of each quadratic relation. Then, sketch its graph.

```
\displaystyle
y = x^2 +8x + 12
```

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Q7a

Find the x-intercepts and the vertex of each quadratic relation. Then, sketch its graph.

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

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Q7b

Find the x-intercepts and the vertex of each quadratic relation. Then, sketch its graph.

```
\displaystyle
y = -x^2 -6x + 27
```

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Q7c

Find the x-intercepts and the vertex of each quadratic relation. Then, sketch its graph.

```
\displaystyle
y = 3x^2 + 10x + 8
```

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Q7d

Find the x-intercepts and the vertex of each quadratic relation. Then, sketch its graph.

```
\displaystyle
y = -x^2 - 3x
```

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Q7e

Find the x-intercepts and the vertex of each quadratic relation. Then, sketch its graph.

```
\displaystyle
y = x^2 -4
```

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Q7f

If two different quadratic relations have the same zeros, will they necessarily have the same axis of symmetry? Will they have the same vertex? Explain your reasoning.

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Q8

Find the value(s] of k so that the parabola has only one x-intercept.

```
\displaystyle
y =x^2 + kx + 100
```

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Q9a

Find the value(s] of k so that the parabola has only one x-intercept.

```
\displaystyle
y = -4x^2 + 28x + k
```

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Q9b

Use the quadratic formula to solve the equation. Express your answers as exact roots.

```
\displaystyle
-3x^2 + 2x + 5 = 0
```

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Q10a

Use the quadratic formula to solve the equation. Express your answers as exact roots.

```
\displaystyle
9x^2 -8x -3 = 0
```

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Q10b

Use the quadratic formula to solve the equation. Express your answers as exact roots.

```
\displaystyle
5x^2 + 7x + 1 = 0
```

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Q10c

Use the quadratic formula to solve the equation. Express your answers as exact roots.

```
\displaystyle
25x^2 + 90x + 81 = 0
```

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Q10d

If a baseball is batted at an angle of 35° to the ground, the distance the ball travels
can be estimated using the equation
`d = 0.0034s^2 + 0.004s - 0.3`

, where sis the
bat speed, in kilometres per hour, and `d`

is the distance flown. in metres. At what speed
does the batter need to hit the ball in order to have a home run where the ball flies
`125`

m? Round to the nearest tenth.

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Q11

A d1ver bounces off a 3-m springboard at an initial upward speed of 4 m/s.

a) Create a quadratic model for the height of the diver above the water.

b) After how many seconds does the diver enter the water? Round to the nearest hundredth of a second.

c) Over what time interval is the height of the diver greater than 3.5 m above the water? Round to the nearest hundredth of a second.

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Q12

A rectangular garden measures 5 m by 7 m. Both dimensions are to be extended at both ends by the same amount so that the area of the garden is doubled. By how much should the dimensions increase. to the nearest tenth of a metre?

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Q13

The Sticker Warehouse sells rolls of stickers for $4.00 each. The average customer buys six rolls of stickers. The owner finds that, for every $0.25 decrease in price. the average customer buys an additional roll.

a) Total sales revenue is the product of the number of units sold and the price. Make an algebraic model to represent The Sticker Warehouse's total revenue per customer.

b) With how many price reductions will the revenue per customer be $30?

c) What is the maximum predicted sales revenue per customer? With how many price reductions will this occur?

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Q14