Chapter 4 Section 4-1 Solving Quadratic Equations in Calculator

Objectives I can find the x-intercepts (zeros) or solutions (roots) of a quadratic with a calculator I can find the vertex point of a quadratic with a calculator

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 bx is the linear term c is the constant term The graph of any quadratic function is a parabola!

Vocabulary versus Answer Format Solutions and Roots have the same answer format: x = Zeros and x-intercepts have the same answer format as ordered pairs (x int, 0)

y = -2x 2 + 4x - 8 Find AOS? Then Vertex Point? a = -2, b = 4, c = -8 AOS: x = -b/2a = -4/2(-2) = -4/-4 = 1 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)

Calculator Help Calculator will find both the vertex and zeros. Once you graph the equation, select 2 nd, Trace Choose 2 for finding zeros Choose either 3 or 4 to find vertex. In all cases you must establish a left and right boundary.

2 nd Trace

Finding Solutions or Zeros First type the equation into y 1 =x 2 – 4x – 4 Then Graph

Finding Solutions or Zeros To find solutions or zeros Select 2 nd Trace #2 It says Left Bound? Move cursor to the left of the zero you want to find Then ENTER

Finding Solutions or Zeros Screen now says Right Bound? Establish the right boundary with the cursor and press ENTER Then press ENTER one more time when it says GUESS?

Finding Solutions or Zeros The screen will appear like this. The cursor will be centered over the solution (zero) It will show the value of the zero in the lower left part of the screen

Finding Vertex Point 2 nd Trace #3 Minimum used when vertex is a min #4 Maximum used when vertex is a max

Finding Vertex Point 2 nd Trace Choose #3 Minimum Screen will look like this Move cursor to the left of the vertex minimum point Press ENTER

Finding Vertex Point Screen will look like this and says Right Bound Move cursor to the right of the vertex minimum point Press ENTER Then ENTER again

Finding Vertex Point Screen will look like this Vertex Point is displayed at the bottom of screen x = 2 y = -8

Homework Worksheet 4-3