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Solutions
22 Videos

Sketch the graph of each equation by correctly applying the required transformation(s) to points on the graph of `y = x^2`

. State the transformation mapping.

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

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1.05mins

Q1a

Sketch the graph of each equation by correctly applying the required transformation(s) to points on the graph of `y = x^2`

. Use a separate grid for each graph.

```
\displaystyle
y =-0.25x^2
```

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1.05mins

Q1b

Sketch the graph of each equation by correctly applying the required transformation(s) to points on the graph of `y = x^2`

. Use a separate grid for each graph.

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

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1.00mins

Q1c

Sketch the graph of each equation by correctly applying the required transformation(s) to points on the graph of `y = x^2`

. Use a separate grid for each graph.

```
\displaystyle
y = \frac{2}{3}x^2
```

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0.56mins

Q1d

Describe the transformation(s) that were applied to the graph of `y = x^2`

to obtain the
graph not labelled `y = x^2`

. Write the equation of the black graph.

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0.37mins

Q2a

`y = x^2`

to obtain the
graph not labelled `y = x^2`

. Write the equation of the black graph.

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0.23mins

Q2b

Determine the values of `h`

and `k`

for each ofthe following transformations. Write the equation in the form `y = (x - b)^2 + k`

. Sketch the graph.

The parabola moves 3 units down and 2 units right.

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0.23mins

Q3a

Determine the values of `h`

and `k`

for each ofthe following transformations. Write the equation in the form `y = (x - b)^2 + k`

. Sketch the graph.

The parabola moves 4 units left and 6 units up.

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0.28mins

Q3b

Describe the transformations in order that you would apply to the graph of `y = x^2`

to sketch each quadratic relation.

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

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0.56mins

Q5a

Describe the transformations in order that you would apply to the graph of `y = x^2`

to sketch each quadratic relation.

```
\displaystyle
y = \frac{1}{2}(x + 3)^2 - 8
```

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0.49mins

Q5b

Describe the transformations in order that you would apply to the graph of `y = x^2`

to sketch each quadratic relation.

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

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0.36mins

Q5c

`y = x^2`

to sketch each quadratic relation.

```
\displaystyle
y = \frac{2}{3}x^2 -1
```

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0.38mins

Q5d

Sketch the graphs below.

```
\displaystyle
y = \frac{1}{2}(x + 3)^2 - 8
```

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1.10mins

Q6a

Sketch the graphs below.

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

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1.38mins

Q6b

Sketch the graphs below.

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

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1.21mins

Q6c

Sketch the graphs below.

```
\displaystyle
y = \frac{2}{3}x^2 -1
```

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1.20mins

Q6d

For each quadratic relation,

- state the stretch/compression factor and the horizontal/vertical translations
- determine whether the graph is reflected m‘ the x—axis
- state the vertex and the equation of the axis of symmetry

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

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1.20mins

Q7a

For each quadratic relation,

- state the stretch/compression factor and the horizontal/vertical translations
- determine whether the graph is reflected m‘ the x—axis
- state the vertex and the equation of the axis of symmetry

```
\displaystyle
y = -\frac{1}{2}(x+ 4)^2
```

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1.56mins

Q7b

For each quadratic relation,

- state the stretch/compression factor and the horizontal/vertical translations
- determine whether the graph is reflected m‘ the x—axis
- state the vertex and the equation of the axis of symmetry

```
\displaystyle
y = 2(x+ 1)^2 - 8
```

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1.43mins

Q7c

For each quadratic relation,

- state the stretch/compression factor and the horizontal/vertical translations
- determine whether the graph is reflected m‘ the x—axis
- state the vertex and the equation of the axis of symmetry

```
\displaystyle
y = -0.25x^2 + 5
```

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0.00mins

Q7d

A parabola lies in only two quadrants. What does this tell you about the values of `a, h`

and `k`

. Explain your thinking, and provide the equation of a parabola as an example.

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0.51mins

Q8