WARM UP 3 EVALUATING RADICAL EXPRESSIONS Evaluate the radical expression when a = -1 and b = 5. (LESSON 9.1). b 2 − 11a b 2 +9a a 2 +8.

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Presentation transcript:

WARM UP 3 EVALUATING RADICAL EXPRESSIONS Evaluate the radical expression when a = -1 and b = 5. (LESSON 9.1). b 2 − 11a b 2 +9a a 2 +8

WARM UP 2 EVALUATING RADICAL EXPRESSIONS Evaluate the radical expression when a = -1 and b = 5. (LESSON 9.1). b 2 − 11a b 2 +9a a 2 +8

WARM UP 1 EVALUATING RADICAL EXPRESSIONS Evaluate the radical expression when a = -1 and b = 5. (LESSON 9.1). b 2 − 11a b 2 +9a a 2 +8

WARM UP EVALUATING RADICAL EXPRESSIONS Evaluate the radical expression when a = -1 and b = 5. (LESSON 9.1). b 2 − 11a b 2 +9a a 2 +8

9.5 Solving Quadratic Equations by Graphing ESTIMATING SOLUTIONS BY GRAPHING The solutions of a quadratic equation in one variable x can be estimated by graphing. Use the following steps: STEP 1 Write the equation in the standard for ax2 +bx + c = 0 STEP 2 Sketch the graph of the related quadratic function y = ax2 +bx + c STEP 3 Estimate the values of the x-intercepts, if any. The solutions, or roots, of ax2 +bx + c = 0 are the x-intercepts of the graph.

9.5 Solving Quadratic Equations by Graphing Solve an Equation by Graphing 1. x2 + 2x = 3 x y x -3 -2 -1 1 y -4 x-intercept (-3, 0) x-intercept (1, 0) y = x2 + 2x - 3

9.5 Solving Quadratic Equations by Graphing Solve an Equation by Graphing 2. x2 - x = 12 In order to fit all of the function on the graph, you must scale the y’s by 2. (+20 at top, -20 at bottom.) x y x -3 -2 -1 𝟏 𝟐 1 2 3 4 y -6 -10 -12 -12.25 x-intercept (-3, 0) x-intercept (4, 0) y = x2 - x - 12

9.5 Solving Quadratic Equations by Graphing Solve an Equation by Graphing 3. -4x2 - 8x = -12 In order to fit all of the function on the graph, you must scale the y’s by 2. (+20 at top, -20 at bottom.) x -3 -2 -1 1 y 12 16 x y y = -4x2 - 8x + 12 x-intercept (-3, 0) x-intercept (1, 0)