1 8 solve quadratic equations by using the quadratic formula and the discriminate September with 16, 2016 notes.noteb
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1 WARM UP 1. Write 15x 2 + 6x = 14x 2 12 in standard form. ANSWER x 2 + 6x +12 = 0 2. Evaluate b 2 4ac when a = 3, b = 6, and c = 5. ANSWER A student is solving an equation by completing the square. Write the step in the solution that appears just before (x 3) = 5. ANSWER (x 3) 2 = 25
2 quadratic formula can be used to solve all quadratic equations Solve an equation with two REAL solutions STEPS 1. Write original equation in standard form. 2. Identify a, b, and c. 3. Write Quadratic Formula. 4. Substitute values for variables in formula. 5. Simplify.
3 Solve an equation with two real solutions EXAMPLE: Solve x 2 + 3x = 2 x 2 + 3x 2 = 0 a = 1, b = 3, c = 2 ANSWER The solutions are and CHECK Use graphing calculator to check solutons
4 EXAMPLE Solve an equation with one real solution Solve 25x 2 18x = 12x 9. Write in standard form. Identify a, b, and c. write quadratic formula substitute values for a, b, and c simplify a = 25, b = 30, c = 9 ANSWER The solution is CHECK Use graphing calculator to check the solution.
5 YOU TRY 1. x 2 = 6x x 2 10x = 2x 9
6 EXAMPLE Solve an equation with imaginary solutions Solve x 2 + 4x = 5 Write in standard form Identify a, b, and c. a = 1, b = 4, c = 5 Substitute and simplify. Rewrite using the imaginary unit i. Simplify. ANSWER The solutions are 2 + i and 2 i. CHECK Use graphing calculator to check solutions.check
7 YOU TRY 3. 7x 5x 2 4 = 2x + 3 ANSWER
8 Use the discriminant CONSIDER Suppose the radicand, b 2 4ac, is negative. What do you know about the solution(s)? Suppose the radicand, b 2 4ac, is zero. What do you know about the solution(s)? Suppose the radicand, b 2 4ac, is positive. What do you know about the solution(s)? discriminant a relatively simple expression that determines the nature of the roots of a given equation or function. POSITIVE Two real roots/solutions ZERO One real root/solution NEGATIVE Two imaginary roots/solutions
9 Find the discriminant of the quadratic equation. Give the number and type of solutions of the equation. USE a. x 2 8x + 17 = 0 ( 8) 2 4(1)(17) = 4 Two imaginary: 4 + i b. x 2 8x + 16 = 0 ( 8) 2 4(1)(16) = 0 One real: 4 c. x 2 8x + 15 = 0 ( 8) 2 4(1)(15) = 4 Two real: 3,5
10 HOMEWORK Textbook page 62, column 2 page 63, #'s 52 54
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