Download presentation

Presentation is loading. Please wait.

1
Vertex Form November 10, 2014 Page 34-35 in Notes

2
Objective relate representations of quadratic functions, such as algebraic, tabular, graphical, and verbal descriptions[6.B]

3
Essential Question What parts of a quadratic function can I determine from the vertex form?

4
Vocabulary parabola: the shape of a quadratic function vertex: the highest or lowest point on a parabola y-intercept: the point where the graph crosses the y-axis x-intercepts: the points where the graph crosses the x-axis axis of symmetry: the vertical line that divides a parabola in two equal parts

5
Vertex Form f(x) = a(x – h) 2 + k – “a” reflection across the x-axis and/or vertical stretch or compression – “h” horizontal translation – “k”: vertical translation

6
What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k h k Vertex: (h, k) Axis of symmetry: x = h y-intercept: (0, y)

7
What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 h k Vertex: (h, k) Axis of symmetry: x = h y-intercept: (0, y)

8
What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 h2 k Vertex: (h, k) Axis of symmetry: x = h y-intercept: (0, y)

9
What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 h2 k0 Vertex: (h, k) Axis of symmetry: x = h y-intercept: (0, y)

10
What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 h2 k0 Vertex: (h, k) (2, 0) Axis of symmetry: x = h y-intercept: (0, y)

11
What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 h2 k0 Vertex: (h, k) (2, 0) Axis of symmetry: x = h x = 2 y-intercept: (0, y)

12
What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 h2 k0 Vertex: (h, k) (2, 0) Axis of symmetry: x = h x = 2 y-intercept: (0, y) (0, 4)

13
What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 y = (x+3) 2 – 1 h2 k0 Vertex: (h, k) (2, 0) Axis of symmetry: x = h x = 2 y-intercept: (0, y) (0, 4)

14
What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 y = (x+3) 2 – 1 h2-3 k0 Vertex: (h, k) (2, 0) Axis of symmetry: x = h x = 2 y-intercept: (0, y) (0, 4)

15
What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 y = (x+3) 2 – 1 h2-3 k0 Vertex: (h, k) (2, 0) Axis of symmetry: x = h x = 2 y-intercept: (0, y) (0, 4)

16
What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 y = (x+3) 2 – 1 h2-3 k0 Vertex: (h, k) (2, 0)(-3, -1) Axis of symmetry: x = h x = 2 y-intercept: (0, y) (0, 4)

17
What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 y = (x+3) 2 – 1 h2-3 k0 Vertex: (h, k) (2, 0)(-3, -1) Axis of symmetry: x = h x = 2x = -3 y-intercept: (0, y) (0, 4)

18
What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 y = (x+3) 2 – 1 h2-3 k0 Vertex: (h, k) (2, 0)(-3, -1) Axis of symmetry: x = h x = 2x = -3 y-intercept: (0, y) (0, 4)(0, 8)

19
What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 y = (x+3) 2 – 1y= -3(x+2) 2 +4 h2-3 k0 Vertex: (h, k) (2, 0)(-3, -1) Axis of symmetry: x = h x = 2x = -3 y-intercept: (0, y) (0, 4)(0, 8)

20
What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 y = (x+3) 2 – 1y= -3(x+2) 2 +4 h2-3-2 k0 Vertex: (h, k) (2, 0)(-3, -1) Axis of symmetry: x = h x = 2x = -3 y-intercept: (0, y) (0, 4)(0, 8)

21
What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 y = (x+3) 2 – 1y= -3(x+2) 2 +4 h2-3-2 k04 Vertex: (h, k) (2, 0)(-3, -1) Axis of symmetry: x = h x = 2x = -3 y-intercept: (0, y) (0, 4)(0, 8)

22
What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 y = (x+3) 2 – 1y= -3(x+2) 2 +4 h2-3-2 k04 Vertex: (h, k) (2, 0)(-3, -1)(-2, 4) Axis of symmetry: x = h x = 2x = -3 y-intercept: (0, y) (0, 4)(0, 8)

23
What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 y = (x+3) 2 – 1y= -3(x+2) 2 +4 h2-3-2 k04 Vertex: (h, k) (2, 0)(-3, -1)(-2, 4) Axis of symmetry: x = h x = 2x = -3x = -2 y-intercept: (0, y) (0, 4)(0, 8)

24
What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 y = (x+3) 2 – 1y= -3(x+2) 2 +4 h2-3-2 k04 Vertex: (h, k) (2, 0)(-3, -1)(-2, 4) Axis of symmetry: x = h x = 2x = -3x = -2 y-intercept: (0, y) (0, 4)(0, 8)(0, -8)

25
What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 y = (x+3) 2 – 1y= -3(x+2) 2 +4y= 2(x+3) 2 +1 h2-3-2 k04 Vertex: (h, k) (2, 0)(-3, -1)(-2, 4) Axis of symmetry: x = h x = 2x = -3x = -2 y-intercept: (0, y) (0, 4)(0, 8)(0, -8)

26
What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 y = (x+3) 2 – 1y= -3(x+2) 2 +4y= 2(x+3) 2 +1 h2-3-2-3 k04 Vertex: (h, k) (2, 0)(-3, -1)(-2, 4) Axis of symmetry: x = h x = 2x = -3x = -2 y-intercept: (0, y) (0, 4)(0, 8)(0, -8)

27
What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 y = (x+3) 2 – 1y= -3(x+2) 2 +4y= 2(x+3) 2 +1 h2-3-2-3 k041 Vertex: (h, k) (2, 0)(-3, -1)(-2, 4) Axis of symmetry: x = h x = 2x = -3x = -2 y-intercept: (0, y) (0, 4)(0, 8)(0, -8)

28
What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 y = (x+3) 2 – 1y= -3(x+2) 2 +4y= 2(x+3) 2 +1 h2-3-2-3 k041 Vertex: (h, k) (2, 0)(-3, -1)(-2, 4)(-3, 1) Axis of symmetry: x = h x = 2x = -3x = -2 y-intercept: (0, y) (0, 4)(0, 8)(0, -8)

29
What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 y = (x+3) 2 – 1y= -3(x+2) 2 +4y= 2(x+3) 2 +1 h2-3-2-3 k041 Vertex: (h, k) (2, 0)(-3, -1)(-2, 4)(-3, 1) Axis of symmetry: x = h x = 2x = -3x = -2x = -3 y-intercept: (0, y) (0, 4)(0, 8)(0, -8)

30
What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 y = (x+3) 2 – 1y= -3(x+2) 2 +4y= 2(x+3) 2 +1 h2-3-2-3 k041 Vertex: (h, k) (2, 0)(-3, -1)(-2, 4)(-3, 1) Axis of symmetry: x = h x = 2x = -3x = -2x = -3 y-intercept: (0, y) (0, 4)(0, 8)(0, -8)(0, 19)

31
To Graph from Vertex Form: 1.Identify the vertex and axis of symmetry and graph. 2.Find the y-intercept and graph along with its reflection. 3.Make a table (with the vertex in the middle) to calculate at least 5 points on the parabola.

32
Example 1 (Left Side): y = (x + 3) 2 - 1 h:_______ k:_______ vertex:__________ axis of symmetry: ___________ y-int: ________ xy -3(-3, -1) x = -3 y = (x + 3) 2 – 1 y = (0 + 3) 2 – 1 y = (3) 2 – 1 y = 9 – 1 y = 8 (0, 8) -3 -1 -4 0 -5 3 -2 0 -1 3

33
y = -3(x – 2) 2 + 4 y = -3(0 – 2) 2 + 4 y = -3(-2) 2 + 4 y = -3 4 + 4 y = -8 Example 2 (Left Side): y = -3(x – 2) 2 + 4 h:_______ k:_______ vertex:__________ axis of symmetry: ___________ y-int: ________ 24(2, 4) x = 2(0, -8) 2 4 1 1 0 -8 3 1 4 -8 xy

34
Assignment 1.f(x) = x 2 – 2 2.g(x) = -(x – 4) 2 3.h(x) = (x + 1) 2 – 3 4.j(x) = (x + 2) 2 + 2

36
Reflection 1.How do you know if a parabola will open upward or downward? 2.When does the parabola have a maximum point? 3.When does the parabola have a minimum point?

Similar presentations

© 2021 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google