1. Determine if f(x) has a minimum or maximum

2. Find the y-intercept of f(x)

3. Find the equation of the axis of symmetry of f(x)

4. Find the vertex of f(x)

5. Graph f(x)

Warm-Up: January 4, 2012 342 xxxf

Homework Questions?

Solving Quadratic Equations by

GraphingSection 6-2

A quadratic equation is of the form

The solutions of a quadratic equation are called roots.

These same values are the zeros of the related quadratic function.

These same values are also the x-intercepts of the graph of the related quadratic function.

Solving Quadratic Equations

02 cbxax

1. Move all terms to one side, to get f(x)=02. Graph the related quadratic function (as

done in section 6-1).3. Determine where the x-intercepts are.

◦ For integer x-intercepts, state the intercept.◦ For x-intercepts between two integers, state

between which two consecutive integers each x-intercept lies.

4. The values of the x-intercepts are also the values of the roots.

Solving Quadratics by Graphing

Use your graph to determine how many real solutions the quadratic equation has.

Number of Solutions

Example 1 – Solve by Graphing

xx 342

You-Try #2 – Solve by Graphing

442 xx

Find two real numbers whose sum is 4 and whose product is 5, or show that no such numbers exist.

Example 3 – Solve by Graphing

Find two real numbers whose sum is 5 and whose product is -14, or show that no such numbers exist.

You-Try #3 – Solve by Graphing

Solve by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located.

Example 4 – Solve by Graphing 362 xx

Solve by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located.

You-Try #4 – Solve by Graphingxx 322

Page 297 #14-19 all, 21-41 every other odd, 67-72 all

Assignment