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Graphing Parabolas

Graphing Parabolas

Graphing Parabolas

Graphing Parabolas

Presentation

•

Mathematics

•

12th Grade

•

Practice Problem

•

Medium

•

CCSS

HSF-IF.C.7A, HSF.IF.A.2

Standards-aligned

Created by

David Ho

Used 2+ times

FREE Resource

43 Slides • 13 Questions

1

Finite Math

7.3a Graphing Quadratic Functions

2

EQ’s for Friday, October 13, 2023

● How do I graph a Quadratic Function?
● How do I find part of a parabola?

3

Ways to Graph a Quadratic Function (Parabola)

● Plotting Points
● Using Vertex Form
● Using Standard Form

4

Parts of a Parabola

●

Vertex (max or min)

●

Axis of symmetry (line that goes
through vertex)

●

x-intercepts (0, 1, or 2)

●

y-intercept (only 1)

5

Multiple Choice

Question image

The Vertex is a

1

Maximum, because it is the high point on the graph.

2

Minimum, because it is the parabola opens down.

6

Multiple Choice

Question image

The axis of symmetry is

1

x = 2

2

y = 9

3

2

4

undefined

7

Math Response

$f\left(x\right)=2x^2-3x+5$

Evaluate the Quadratic Function for

$f\left(-3\right)$

Type answer here

Correct Answer: 32

Deg^°

Rad

8

Graphing a Quadratic Function by Plotting Points

x

(x,y)

-5

-4

-3

-2

-1

0

1

9

Graphing a Quadratic Function by Plotting Points

(x,y)

(-5, 8)

(-4, 3)

(-3, 0)

(-2, -1)

(-1, 0)

(0, 3)

(1, 8)

10

Draw

Plot the Points of the Parabola

11

Graphing a Quadratic Function by Plotting Points

(x,y)

(-5, 8)

(-4, 3)

(-3, 0)

(-2, -1)

(-1, 0)

(0, 3)

(1, 8)

12

Quadratic Functions

● Using Vertex Form

● Using Standard Form

13

Quadratic Functions

● Using Vertex Form

● Using Standard Form

14

Quadratic Functions

● Using Vertex Form

● Using Standard Form

15

Quadratic Functions

● Using Vertex Form

● Using Standard Form

16

Quadratic Functions

● Using Vertex Form

● Using Standard Form

17

Multiple Choice

Which equation is in vertex form?

1

y = ax^2 + bx + c

2

y = mx + b

3

y = a(x-h)(x-k)

4

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

18

Multiple Choice

Question image

What is the vertex of the parabola?

$f\left(x\right)=2\left(x-3\right)^2+4$

1

(2, 4)

2

(3, 4)

3

(3, 2)

4

(-3, 4)

19

Multiple Choice

Question image

Give the axis of symmetry for the parabola.

$f\left(x\right)=2\left(x+5\right)^2-1$

1

x = 2

2

x = 10

3

x = 0

4

x = -5

5

x = 5

20

Multiple Choice

Question image

What is the axis of symmetry for the parabola?

$f\left(x\right)=2x^2-4x-3$

1

x = 1

2

x = 0

3

x = 2

4

x = -1

21

Multiple Choice

Question image

What is the vertex of the parabola?

$f\left(x\right)=2x^2-4x-3$

1

(1, -5)

2

(0, -3)

3

(1, 5)

4

(2, -3)

22

Graphing a Quadratic Function from Vertex Form

1. Plot the Vertex (h, k)
2. Draw AOS (x = h)
3. Get 2 points, copy to other

side of AOS

4. Sketch the graph

23

1. Plot the Vertex (h, k)
2. Draw AOS (x = h)
3. Get 2 points, copy to other

side of AOS

4. Sketch the graph

24

Multiple Choice

Question image

Give the vertex of the parabola.

1

(-4, 1)

2

(-4, -1)

3

(4, -1)

4

(4, 1)

25

Multiple Choice

Question image

Give the axis of symmetry for the parabola.

$f\left(x\right)=-\frac{1}{2}\left(x+4\right)^2-1$

1

x = -4

2

x = 4

3

x = -2

4

x = -1

26

Multiple Choice

Question image

Give the point on the parabola when x = -2.

1

(-2, -3)

2

(-2, 1)

3

(-2, -1)

4

(-2, -4)

27

Multiple Choice

Question image

Know that the axis of symmetry is x = -4 and (-2, -3) is on the parabola, which point must also be on the parabola?

1

(-4, -5)

2

(-2, -5)

3

(-6, -3)

4

(-8, -3)

28

1. Plot the Vertex (h, k)
2. Draw AOS (x = h)
3. Get 2 points, copy to other

side of AOS

4. Sketch the graph

29

Write the equation of the parabola in Vertex form.

30

Write the equation of the parabola in Vertex form.

31

Graphing a Quadratic Function from Standard Form

1. Draw AOS (x = − b/2a)
2. Plot Vertex (x, f(x))
3. Get 2 points, copy to other

side of AOS

4. Sketch the graph

32

1. Draw AOS (x = − b/2a)
2. Plot Vertex (x, f(x))
3. Get 2 points, copy to other

side of AOS

4. Sketch the graph

33

1. Draw AOS (x = − b/2a)
2. Plot Vertex (x, f(x))
3. Get 2 points, copy to other

side of AOS

4. Sketch the graph

34

35

36

37

38

39

40

41

42

43

44

45

46

Finding a Parabola’s x-intercepts

47

Finding a Parabola’s x-intercepts

48

Finding a Parabola’s y-intercepts

49

Finding a Parabola’s y-intercepts

50

Finding a Parabola’s Axis of Symmetry

51

Finding a Parabola’s Axis of Symmetry

52

Finding a Parabola’s Vertex

53

Finding a Parabola’s Vertex

54

55

56

pattern-tertiary

Finite Math

7.3a Graphing Quadratic Functions

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