Do Now Find the value of y when x = -1, 0, and 2. y = x2 + 3x – 2

2.2: Characteristics of Quadratic Functions Objective: graph quadratic functions and identify their vertex and axis of symmetry

Axis of symmetry The axis of symmetry is a line that divides a parabola into mirror images and passes through the vertex. Cuts a parabola in half

Example 1: Plot the vertex at (- 3, 4).   Plot the vertex at (- 3, 4). The axis of symmetry will be at the line vertically along the x value of the vertex. x = -3 Plot two more points on the graph (- 2, 2) and (- 1, - 4) Draw the parabola through the points.

Practice Graph y = 3(x - 2)2 + 1. Label the vertex and axis of symmetry.

Quadratic Functions  

Quadratic Equation Standard Form: f(x) = ax2 + bx + c Equation for the line of symmetry: x-coordinate of vertex (find y-value by plugging in x-value and solving):

Steps to graphing a quadratic equation in standard form: Standard form: f(x) = ax2 + bx + c 1.) Find x-coordinate of the vertex: 2.) Create table with x-coordinate of vertex in the middle and choose at least one value smaller than vertex and one value larger than vertex for x. 3.) Plug in values for x and solve for y. 4.) Plot points and draw parabola.

Graph f(x) = -4x2 + 8x+ 2

Quadratic Equation  

Graphing using intercept form f(x) = a(x – p)(x – q) Plot the x-intercepts: points p and q Find x-coordinate of vertex by averaging p and q: Find y-coordinate of vertex by plugging in x-coordinate and solving. Plot the vertex.

Graph f(x) = (x + 2)(x – 2)

Graph y = 3(x + 3)(x + 5)

Finding Maximum and Minimum Values  

Find the Maximum or Minimum Value  

Find the Maximum or Minimum Value  

Homework: Textbook pg. 61-63 # 9, 29, 41, 56