WARM UP 1) Complete the square x 2 – 14x + ____ 2) Solve by completing the square x 2 + 10x + 14 = 0.

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Presentation transcript:

WARM UP 1) Complete the square x 2 – 14x + ____ 2) Solve by completing the square x x + 14 = 0

HW CHECK – 5.7

THE QUADRATIC FORMULA SECTION 5.8

THE QUADRATIC FORMULA A quadratic equation in standard form ax 2 + bx + c = 0 can be solved with:

EXAMPLE 1: USING THE QUADRATIC FORMULA Step 1) Write in standard form. Step 2) Find the values of a, b, and c. Step 3) Use the Quadratic Formula. Step 4) Simplify. The Quadratic Formula!

EXAMPLE 2: USING THE QUADRATIC FORMULA Step 1) Write in standard form. Step 2) Find the values of a, b, and c. Step 3) Use the Quadratic Formula. Step 4) Simplify. The Quadratic Formula!

EXAMPLE 3: USING THE QUADRATIC FORMULA Step 1) Write in standard form. Step 2) Find the values of a, b, and c. Step 3) Use the Quadratic Formula. Step 4) Simplify. The Quadratic Formula!

USING THE DISCRIMINANT Quadratic equations can have real or complex solutions. You can determine the type and number of solutions by finding the discriminant. The discriminant of a quadratic equation in the form ax 2 + bx + c = 0 is the value of the expression b 2 – 4ac. Discriminant

USING THE DISCRIMINANT Value of the DiscriminantType and Number of Solutions for ax 2 + bx + c =0 Examples of Graphs of Related Functions y = ax 2 + bx + c b 2 – 4ac > 0 Two real solutionsTwo x-intercepts b 2 – 4ac = 0 One real solutionOne x-intercept b 2 – 4ac < 0 No real solutionsNo x-intercepts Is this possible? If so, what are the possible answers?

EXAMPLE 5: USING THE DISCRIMINANT Determine the type and number of solutions.

CLASSWORK – TURN IN WHEN COMPLETE! 1) x 2 – 4x + 3 = 0 2) x 2 = 3x – 1 3) 8x 2 – 2x – 3 = 0

COMING UP… Homework tonight – Worksheet 5.8 # 1, 4, 7, 16, 17, 21 Unit 5 Test Friday