9.3 Graphing Quadratic Functions Algebra 9.3 Graphing Quadratic Functions

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

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.

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.

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

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 =

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

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 -8 + 8 = 4 VERTEX: (-2, 4)

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.

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

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

A Few together from the Homework pg. 521 # 5 and #15

Homework pg. 521 # 1-15