Section1.4 QUADRATIC EQUATIONS This presentation is base on Power Point slides found at with modifications by Jeffrey Linek Ed. D.

Quadratic Equations We can solve quadratic equations –Graphically –Algebraically by factoring –Using the Completing the Square Method –Extracting a Zero or Root –Using the Quadratic Formula

Solution Set:

Solve:  x  Solution set: {-7, 3}

Solve by completing the square:

Theorem Quadratic Formula

Discriminant of a Quadratic Equation

Quadratic Equations Solve the following equation graphically. x = x + 6

Solve the following equation graphically. x = x + 6 On the TI-83 press the Y= key and enter the equations Y 1 = x and Y 2 = x + 6

Solve the following equation graphically. x = x + 6 Press the GRAPH key. The points of intersection are the solutions to the problem. We will use the intersect feature to find their values.

Solve the following equation graphically. x = x + 6 TI-83: The Intersect Feature Press the 2 nd key, then the TRACE key Select 5: intersect Then, press the ENTER key

Solve the following equation graphically. x = x + 6 TI-83: The Intersect Feature The graph of the two equations will be displayed. The TI-83 will ask if the cursor is on the first graph. Press the ENTER key. Next, the TI-83 will ask if the cursor is on the second graph. Press the ENTER key.

Solve the following equation graphically. x = x + 6 TI-83: The Intersect Feature Notice that the calculator asks you to guess at the answer, and that the cursor is midway between the two points of intersection. We will just press the ENTER key to see what happens.

Solve the following equation graphically. x = x + 6 TI-83: The Intersect Feature Notice that the TI-83 solved for one of the points of intersection, namely, (-2.702, 3.298). We need to find the other point as well.

Solve the following equation graphically. x = x + 6 TI-83: The Intersect Feature oAs we did earlier press the 2 nd Key, the Trace Key, then the number 5 Key for 5: intersect. oOnce again the calculator will ask if the cursor is on the first graph. This time, use the key to move the cursor closed to the point of intersection. Then, press the ENTER key >

Solve the following equation graphically. x = x + 6 TI-83: The Intersect Feature The TI-83 will ask if the cursor is on the second graph. Press the ENTER key.

Solve the following equation graphically. x = x + 6 TI-83: The Intersect Feature The calculator asks you to guess at the answer. We will just press the ENTER key to get the answer.

Solve the following equation graphically. x = x + 6 TI-83: The Intersect Feature The answer (3.702, 9.702) appears. However, we need to interpret the answer because our original equation did not contain y.

Solve the following equation graphically. x = x + 6 The answers. Remember that original we set Y 1 = x and Y 2 = x + 6. Therefore, Y 1 = Y 2 since, x = x + 6 Y 1 and Y 2 are result of placing a value for x into the equation x = x + 6 So, our answers are x = or x = 3.702

Now, solve the equation algebraically x = x + 6