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 = ax2 + bx + c, where a 0

• ax2 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

• (xint , 0)

y = -2x2 + 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 = -2 + 4 – 8

• y = -6

• Vertex (1, -6)

Calculator Help

• Calculator will find both the vertex and zeros.

• Once you graph the equation, select 2nd, 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.

2nd Trace

Finding Solutions or Zeros

• First type the equation into

• y1 =x2 – 4x – 4

• Then Graph

Finding Solutions or Zeros• To find

solutions or zeros

• Select • 2nd 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

• 2nd Trace

• #3 Minimum used when vertex is a min

• #4 Maximum used when vertex is a max

Finding Vertex Point

• 2nd 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