## Discussion

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### Solving Equations by Graphing

A

*quadratic equation*is one that can be written in the form ax^{2}+ bx + c = 0, where a ≠ 0. Its solutions are called the*roots*of the equation.The roots of a quadratic equation are x-intercepts of the graph of the related quadratic function.

A quadratic equation has 2 real roots if its graph has two x-intercepts, 1 real root if it has one x-intercept (in this case, the graph is tangent to the x axis and the root is called a

*double root*), and no real roots if it has no x-intercepts.If a root is not an integer, estimate the root by stating the two consecutive integers it lies between.

In general, use graphing to solve an equation only if you would be satisfied with an estimate for the solutions, not exact values.

A real number is a zero of the quadratic function f(x) if and only if it is a root of the equation f(x) = 0.

### Solving Equations by Graphing

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro 0:00
- Solving a Quadratic Equation 0:22
- Example
- Two Distinct Solutions/Roots 5:08
- One Double Root 5:58
- No Real Roots 7:14
- Estimating Solutions 8:00
- Example
- Example
- Lecture Example 1 9:43
- Lecture Example 2 14:10
- Additional Example 3
- Additional Example 4

1 answer

Last reply by: Manuela Fridman

Sat Oct 8, 2011 7:19 PM

Post by julius mogyorossy on September 20, 2011

Can't see examples 3 and 4 again. Maybe the don't exist.