Warm-up ( ) 1. Multiply with FOIL (2x – 4)(6x – 2) 2. Given y = -2(x – 4) 2 + 5, then find a.Vertex Point? b.AOS? c.y-intercept? d.Opening Direction? e.Graph it?

Chapter 4 Section 4-1 Graphing Quadratic Equations

Objectives I can identify a, b, c from a quadratic equation I can graph Quadratic Functions manually with Data Table, including Axis of Symmetry I can describe the three types of solutions to a quadratic equation

Quadratic Equation A quadratic equation is an equation that can be written in the format y = ax 2 + bx + c, where a  0 ax 2 is the quadratic term that makes it a quadratic

Real World Applications

Vocabulary versus Answer Format Solutions and Roots have the same answer format: x = or in braces {} x = 3, 5{3, 5} Zeros and x-intercepts have the same answer format as ordered pairs (x int, 0) (3, 0) and (5, 0)

Axis of Symmetry The axis of symmetry can be found by the following equation:

y = 3x 2 - 2x - 1 Find AOS? a = 3, b = -2, c = -1 AOS:

y = -2x 2 + 4x - 8 Find AOS? a = -2, b = 4, c = -8 AOS:

Finding the Vertex Point If the AOS is x = 1, then the Vertex Point is Vertex (1, ?) How can I find the y-value? PLUG the x-value back into the equation for all x’s and solve for “y”

y = -2x 2 + 4x - 8 AOS: x = 1 Now use this x-value to find the vertex point y = -2(1) 2 + 4(1) – 8 y = – 8 y = -6 Vertex (1, -6)

Putting it ALL together to GRAPH

Example Let’s graph y = 2x 2 + 4x – 5 So we need: 1. AOS 2. Vertex Point 3. More points to graph

Homework Worksheet 4-2