2U

Name

Non-Linear Relationships 1 Y10 Maths

This is a Sample Workbook. All sections have been left blank and they are filled under the guidance of a

teacher in a Project Academy Class.

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Non-Linear Functions

The Parabola

The general form

The vertex form

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Sketching parabolas

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2

3

4

Question 8Sketch the parabola y = x2 + 3x − 4

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Question 9Sketch the parabola y = − x2 + 4x

Question 10Sketch the parabola , by first putting the equation in vertex form.y = − x2 + 4x

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How does completing the square work?

Completing the square: The method

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2

3

4

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Question 11(a) Use the method of completing the square to evaluate:

i.

ii.

(b) Hence, graph

i.

ii.

y = x2 + 4x + 1

y = x2 + 3x + 3

x2 + 3x + 3 = 0

x2 + 4x + 1 = 0

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A better way to find the x-intercepts?

The Quadratic Formula:

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Question 12

(a) Use the Quadratic Formula to find the x-intercepts of the following

i.

ii.

iii.

(b) Hence, graph them :)

y = − 3x2 − x + 4

y = x2 − 8x + 16

y = − x2 + 4x + 4

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Extra Writing Space

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Extra Writing Space

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The Circle

The actual definition of a circle:

The Cartesian Equation for a Circle:

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Question 15

(a) Sketch the graph of

(b) A point P(x,y) moves such that it is always 3 units away from the point A(3,0). Draw the path this point follows.

x2 + (y + 5)2 = 16

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Question 16

Graph . x2 − 2x + y2 − 4y − 4 = 0

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Semicircles

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Question 17

(a) Graph the following semicircles

i.

ii.

iii. x = 36 − x2

y = 9 − x2

y = − 9 − x2

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Extra Writing Space

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The Exponential Curve

The milk & tea conundrumYou’re at home making yourself a nice cup of tea. Just as you’re about to pour the milk into your tea, you get

an important phone call. You want the warmest possible cup of tea so should you put the milk into the tea

before or after the phone call?

Circle one:

Before Phone Call / After Phone

We’ll answer this soon!

The exponential function

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Some Cool TransformationsSome Cool Transformations

The Friend-zone Asymptote

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Question 18(a) Graph the following exponential functions

i.

ii.

iii. y = − 5−x

y = 4x

y = (14 )

x

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So before or after the phone call?After learning a bit about the exponential function, have you changed your guess?

Circle one:

Before Phone Call / After Phone Call

The explanation.

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The Hyperbola

Enter the Hyperbola.

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Some Cool TransformationsSome Cool Transformations

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Question 19

Question 20

Sketch the hyperbola y = 1x − 4

Sketch the hyperbola y = 4x − 3 + 2

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Extra Writing Space

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Notes

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Notes