Download presentation

1
**9.3 Graphing Quadratic Functions**

Algebra 9.3 Graphing Quadratic Functions

2
**CLASSIFYING EQUATIONS**

y = 2x²+ 7x + 3 y = 2x + 4 What is the pattern ? y = 5x² y = 5x y = x² - 4 y = x - 4 LINEAR QUADRATIC

3
**Standard Form of a Quadratic Equation**

y = ax²+ bx + c (a ≠ 0) An equation is called QUADRATIC if it has a squared variable There MUST be a squared variable. There may or may not be the “middle term” or the constant.

4
**Every quadratic function has a U-shaped graph called a parabola.**

vertex ● ● vertex The vertex of a parabola is the lowest point of a parabola that opens up and the highest point of a parabola that opens down.

5
The axis of symmetry of a parabola is the line passing through the vertex that divides the parabola into two symmetric parts. vertex ● ● vertex axis of symmetry axis of symmetry

6
**Identifying a, b and c y = ax²+ bx + c (a ≠ 0) In y = 2x²+ 3x – 5 a =**

-5 In y = -x²- 5x + 2 a = -1 b = -5 c = 2 In y = x²- 3x a = 1 b = -3 c = In y = -x²+ 4 a = -1 b = c = 4 In y = -3x² a = -3 b = c =

7
**The effect of a on the parabola**

y = x²+ 2x + 1 y = -x²+ 2x + 1 a = 1 a = -1 If a is positive the parabola opens up If a is negative the parabola opens down

8
**Finding the vertex In the equation y = ax²+ bx + c**

● In the equation y = ax²+ bx + c the x coordinate of the vertex can be found using the formula: Then substitute the x value into the original equation to find the y coordinate In y = x²+ 4x + 8 a = 1 b = 4 c = 8 y = (-2)² + 4(-2) + 8 VERTEX: x = y = = 4 VERTEX: (-2, 4)

9
**Graphing a Quadratic Function**

STEPS Find the x coordinate of the vertex: Draw the line of symmetry at the x-value. Then substitute the x value to find y. The vertex will be an ordered pair (x,y). x = Make an x/y table. Choose x values to the left and right of the vertex. Plot as you go. Connect the points as a smooth curve.

10
**x y Graph: y = x²- 2x - 3 = = 1 Vertex: x = y = (1)² - 2(1) – 3 = -4**

-1 ● ● x -3 1 -4 ● ● 2 -3 ● 3

11
**x y Graph: y = -x²+ 2x - 3 = = 1 Vertex: x = y = -(1)² + 2(1) – 3 = -2**

● -1 -6 ● ● x -3 1 -2 2 -3 ● ● 3 -6

12
**A Few together from the Homework**

pg # 5 and #15

13
Homework pg # 1-15

Similar presentations

© 2020 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