Intro to Parabolas 2

Years

Year 10

Parabolas

Intro to Parabolas

Intro to Parabolas 2

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Question 1 of 5

1. Question
Which of the following shows the graph of $y = x^{2} + 3$ $y=x^2+3$ ?
- 1.
- 2.
- 3.
- 4.
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The Basic Form of a Parabola

$y =$ $y=$ $a$ $a$ $x^{2} +$ $x^2+$ $C$ $C$

Vertex: $(0,$ $(0,$ $C$ $C$ $)$ $)$

First, identify the vertex of the parabola from the equation.

$y$ $y$ $=$ $=$ $a$ $a$ $x^{2} +$ $x^2+$ $C$ $C$

$y$ $y$ $=$ $=$ $($ $($ $1$ $1$ $) x^{2} +$ $)x^2+$ $3$ $3$ Highlight values of $a$ $a$ and $C$ $C$

$a$ $a$ $=$ $=$ $1$ $1$

$C$ $C$ $=$ $=$ $3$ $3$

Vertex is at $(0,$ $(0,$ $C$ $C$ $)$ $)$ , so the graph’s vertex is at $(0,$ $(0,$ $3$ $3$ $)$ $)$ .

Plot the vertex on the graph.

Because the value of $a$ $a$ is positive, the parabola is concave up. Draw a parabola from the vertex.
Question 2 of 5

2. Question
Which of the following shows the graph of $y = x^{2}$ $y=x^2$ ?
- 1.
- 2.
- 3.
- 4.
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The Basic Form of a Parabola

$y =$ $y=$ $a$ $a$ $x^{2} +$ $x^2+$ $C$ $C$

Vertex: $(0,$ $(0,$ $C$ $C$ $)$ $)$

First, identify the vertex of the parabola from the equation.

$y$ $y$ $=$ $=$ $a$ $a$ $x^{2} +$ $x^2+$ $C$ $C$

$y$ $y$ $=$ $=$ $x^{2}$ $x^2$

$y$ $y$ $=$ $=$ $($ $($ $1$ $1$ $) x^{2} +$ $)x^2+$ $0$ $0$ Highlight values of $a$ $a$ and $C$ $C$

$a$ $a$ $=$ $=$ $1$ $1$

$C$ $C$ $=$ $=$ $0$ $0$

Vertex is at $(0,$ $(0,$ $C$ $C$ $)$ $)$ , so the graph’s vertex is at $(0,$ $(0,$ $0$ $0$ $)$ $)$ .

Plot the vertex on the graph.

Because the value of $a$ $a$ is positive, the parabola is concave up. Draw a parabola from the vertex.
Question 3 of 5

3. Question
Which of the following shows the graph of $y = x^{2} - 4$ $y=x^2-4$ ?
- 1.
- 2.
- 3.
- 4.
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The Basic Form of a Parabola

$y =$ $y=$ $a$ $a$ $x^{2} +$ $x^2+$ $C$ $C$

Vertex: $(0,$ $(0,$ $C$ $C$ $)$ $)$

First, identify the vertex of the parabola from the equation.

$y$ $y$ $=$ $=$ $a$ $a$ $x^{2} +$ $x^2+$ $C$ $C$

$y$ $y$ $=$ $=$ $x^{2}$ $x^2$

$y$ $y$ $=$ $=$ $($ $($ $1$ $1$ $) x^{2} + ($ $)x^2+($ $- 4$ $-4$ $)$ $)$ Highlight values of $a$ $a$ and $C$ $C$

$a$ $a$ $=$ $=$ $1$ $1$

$C$ $C$ $=$ $=$ $- 4$ $-4$

Vertex is at $(0,$ $(0,$ $C$ $C$ $)$ $)$ , so the graph’s vertex is at $(0,$ $(0,$ $- 4$ $-4$ $)$ $)$ .

Plot the vertex on the graph.

Because the value of $a$ $a$ is positive, the parabola is concave up. Draw a parabola from the vertex.
Question 4 of 5

4. Question
Which of the following shows the equation of the graph below?
- 1. $y = - \frac{1}{5} x^{2}$ $y=-1/5x^2$
- 2. $y=1/5x^2$
- 3. $y=-5x^2$
- 4. $y=5x^2$
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If $a>0$ , the parabola is concave up.
If $a<0$ , the parabola is concave down.
A big $a$ means a narrow parabola while a small $a$ means it is wide.

A point on the parabola is $($ $2$ , $20$ $)$ .Substitute the values of $x$ and $y$ into the equation for parabola.

$y$ $=$ $a\color{green}{x}^{2}$ Equation of the parabola

$20$ $=$ $a(\color{green}{2})^{2}$ $x=2$ and $y=20$

$20$ $=$ $4a$ Simplify

$5$ $=$ $a$ Divide both sides by $4$

$a$ $=$ $5$

Substitute the value of $a$ back to the equation.

$y$ $=$ $a\color{green}{x}^{2}$ Equation of the parabola

$y$ $=$ $5\color{green}{x}^{2}$ $a=5$

$y$ $=$ $5x^2$

$y=5x^2$

Question 5 of 5

Which of the following shows the equation of the graph below?

1. $y=1/3x^2$
2. $y=-3x^2$
3. $y=3x^2$
4. $y=-1/3x^2$

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If $a>0$ , the parabola is concave up.
If $a<0$ , the parabola is concave down.
A big $a$ means a narrow parabola while a small $a$ means it is wide.

A point on the parabola is

$($ $-3$ , $-3$

$)$ .Substitute the values of $x$ and $y$ into the equation for parabola.

$y$	$=$	$a\color{green}{x}^{2}$	Equation of the parabola
$-3$	$=$	$a(\color{green}{-3})^{2}$	$x=-3$ and $y=-3$
$-3$	$=$	$9a$	Simplify
$-1/3$	$=$	$a$	Divide both sides by $9$

$a$	$=$	$-1/3$

Substitute the value of

$a$ back to the equation.

$y$	$=$	$a\color{green}{x}^{2}$	Equation of the parabola
$y$	$=$	$-\frac{1}{3} \color{green}{x}^{2}$	$a=-1/3$

$y$	$=$	$-1/3x^2$

$y=-1/3x^2$

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Quiz summary

Information

1. Question

Hint

Correct!

The Basic Form of a Parabola

2. Question

Hint

Fantastic!

The Basic Form of a Parabola

3. Question

Nice Job!

The Basic Form of a Parabola

4. Question

Hint

Nice Job!

5. Question

Hint

Well Done!

Quizzes

$y$ $y$	$=$ $=$	$a$ $a$ $x^{2} +$ $x^2+$ $C$ $C$
$y$ $y$	$=$ $=$	$($ $($ $1$ $1$ $) x^{2} +$ $)x^2+$ $3$ $3$	Highlight values of $a$ $a$ and $C$ $C$
$a$ $a$	$=$ $=$	$1$ $1$
$C$ $C$	$=$ $=$	$3$ $3$