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**Section 1.5 Quadratic Equations**

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**Solving Quadratic Equations by Factoring**

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Example Solve by factoring:

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Example Solve by factoring:

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Example Solve by factoring:

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Graphing Calculator The real solutions of a quadratic equation ax2+bx+c=0 correspond to the x-intercepts of the graph. The U shaped graph shown below has two x intercepts. When y=0, the value(s) of x will be the solution to the equation. Since y=0 these are called the zeros of the function.

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**Solving Polynomial Equations using the Graphing Calculator**

By pressing 2nd Trace to get Calc, then the #2,you get the zeros. It will ask you for left and right bounds, and then a guess. For left and right bounds move the blinking cursor (using the arrow keys-cursor keys) to the left and press enter. Then move the cursor to the right of the x intercept and press enter. Press enter when asked to guess. Then you get the zeros or solution. Repeat this process for each x intercept.

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**Solving Quadratic Equations by the Square Root Property**

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Example Solve by the square root property:

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Example Solve by the square root property:

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Completing the Square

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**Why we call this completing the square.**

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Example What term should be added to each binomial so that it becomes a perfect square trinomial? Write and factor the trinomial.

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Example Solve by Completing the Square:

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Example Solve by Completing the Square:

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**Solving Quadratic Equations Using the Quadratic Formula**

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Example Solve by using the Quadratic Formula:

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The Discriminant

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Example Compute the discriminant and determine the number and type of solutions:

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**Determining Which Method to Use**

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Applications

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Example

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Example A 42 inch television is a television whose screen’s diagonal length is 42 inches. If a television’s screen height is 26 inches, find the width of the television screen 42 inches 26 inches

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(a) (b) (c) (d)

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(a) (b) (c) (d)

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