Download presentation

Presentation is loading. Please wait.

Published byAngel Pope Modified over 5 years ago

1
Graphing Quadratics With VERTEX and Axis of Symmetry At the end of the period, you will learn: 1. To compare parabola by the coefficient 2. To find the vertex of a parabola

2
Warm-up Graph the quadratic equation by factoring. Tell whether the quadratic opens upward or downward 1. y = - x 2 + 7x + 12 2. f(x)= x 2 + 21x + 20 3. y = - x 2 - 6x + 8

3
Identifying Vertex f(x) = 2x - x 2 Vertex: (1,1)

4
Identifying Vertex 4 Your turn! 4 f(x) = x 2 - 4 Vertex: (0, -4)

5
Comparing Parabola y x x - axis y - axis Green y = 5x 2 Purple y = ½x 2 Blue y = ¼ x 2 Smaller coefficient = Wider parabola

6
Graphing with vertex Vertex = (__, __) xy (__, __) 0 –4–4 Formula in finding the vertex x = –b_ 2a y = substitute the value of x y = ax 2 + bx + c

7
Example Find the vertex of y = -3x 2 + 6x + 5 Formula in finding the vertex x = –b_ 2a y = substitute the value of x x = –b_ 2a x = –6 2(-3) x = –6 –6–6 x = 1 y = substitute the value of x y = -3x 2 + 6x + 5 y = -3(1) 2 + 6(1) + 5 y = -3 + 6 + 5 y = 8 Vertex = (1, 8)

8
Graph the Parabola y = -3x 2 + 6x + 5 Vertex = (1, 8) y x 2 4 6 8 1 2345

9
Your Turn! Find the vertex of y = x 2 + 2x – 5 Formula in finding the vertex x = –b_ 2a y = substitute the value of x x = –b_ 2a x = –2 2(1) x = –2 2 x = – 1 y = substitute the value of x y = x 2 + 2x – 5 y = 1 - 2 – 5 y = –6 Vertex = (-1, -6) y = ( –1 ) 2 + 2(-1) – 5

10
Graph the Parabola y x 2 4 6 8 1 2345 y = x 2 + 2x – 5 Vertex = (-1, -6)

11
Graphing Quadratics Review on graphing quadratics At the end of the period, you will master: 1. To graph parabola of this form: y = ax 2 + c

12
Classwork Sketch the following parabola by finding the vertex 1. y = x 2 + 4x + 3 5. y = - x 2 + 4x - 4 2. y = –x 2 + 4x – 4 6. y = – x 2 + 8x – 5 4. y = x 2 - 10x + 20 3. y = x 2 + 3

13
Warm-up Find the VERTEX and graph the PARABOLA 1. y = -3x 2 + 6x + 5 Vertex = (1, 8) 2. y = x 2 + 2x – 5 Vertex = (-1, -6) 3. y = x 2 + 4x – 5 Vertex = (-2,-9) 4. y = x 2 – 2 Vertex = (0, –2) Formula in finding the vertex x = –b_ 2a y = substitute the value of x

14
y x Graphing: y = ax 2 + c 4. y = x 2 – 2 Vertex = (0, –2) 5. y = x 2 + 2 Vertex = (0, 2) y x

15
Graphing: y = ax 2 + c 5. y = x 2 + 2 Vertex = (0, 2) y x 6. y = –x 2 + 2 Vertex = (0, 2) y x

16
Classwork Graph the following parabola using: I Finding the solution of the equations (Factoring) II Finding the VERTEX (Using formula) III Graphing on y-axis (using vertex) 1. y = - x 2 - 9x + 20 2. y = x 2 - 6x + 83. y = - x 2 - 7x + 10 3. y = x 2 + 6x - 81. y = x 2 + 4x + 32. y = –x 2 + 4x – 4 1. y = x 2 – 1 2. y = –x 2 + 2 3. y = x 2 - 5 4. y = –x 2 + 3

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