Textbook

10 Principles of Mathematics Nelson
Chapter

Chapter 3
Section

Geometric Properties Mid Chapter Review

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Solutions
17 Videos

State whether each relation is quadratic. Justify your answer.

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Q1a

State whether each relation is quadratic. Justify your answer.

```
\displaystyle
y - 5x^2 + 3x- 1
```

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Q1b

State whether each relation is quadratic. Justify your answer.

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Q1c

Each table of values represents a quadratic relation. Decide, without graphing, whether the parabola opens upward or downward.

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Q2a

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Q2b

Graph `y = -x^2 + 6x`

to determine

a) the equation of the axis of symmetry

b) the coordinates of the vertex

c) the y—intercept

d) the zeros

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Q3

The points `(-3, 8)`

and `(9, 8)`

lie on opposite sides of a parabola. Determine the equation of the axis of symmetry.

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Q4

Determine the y—intercept, zeros, equation of the axis of symmetry, and vertex.

```
\displaystyle
y = x^2 + 8x + 15
```

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Q5a

Determine the y—intercept, zeros, equation of the axis of symmetry, and vertex.

```
\displaystyle
y = -2x^2 + 16x -32
```

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Q5b

A soccer ball is kicked into the air. lts height, I}, in metres, is approximated by the equation `h = -5t^2 + 15t + 0.5`

, where `t`

is the time in seconds since the ball was kicked.

a) From what height is the ball kicked?

b) When does the ball hit the ground?

c) When does the ball reach its maximum height?

d) What is the maximum height of the ball?

e) What is the height of the ball at `t = 3`

?
Is the ball travelling upward or downward at this time? Explain.

f) When is the ball at a height of 10 m?

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Q6

Determine the y-intercept, zeros, equation of the axis of symmetry, and vertex of each quadratic relation. Then sketch its graph.

```
\displaystyle
y = (x-5)(x+ 5)
```

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Q7a

Determine the y-intercept, zeros, equation of the axis of symmetry, and vertex of each quadratic relation. Then sketch its graph.

```
\displaystyle
y = -(x-6)(x-2)
```

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Q7b

Determine the y-intercept, zeros, equation of the axis of symmetry, and vertex of each quadratic relation. Then sketch its graph.

```
\displaystyle
y = 2(x-1)(x+3)
```

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Q7c

```
\displaystyle
y = -0.5(x+4)^2
```

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Q7d

The zeros of a parabola are `-10`

and `30`

. The parabola crosses the y—axis at 50.

a) Determine an equation for the parabola.

b) Determine the coordinates of the vertex.

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Q8

Determine an equation for this quadratic relation.

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Q9

Give an example of an equation of a quadratic relation whose vertex and x—intercept occur at the same point.

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Q10