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WARM UP

WARM UP. 4. PRODUCT OF POWERS Write the expression as a single power of the base (LESSON 8.1). x 2 • x 5 (-5) • (-5) 8 x 2 • x 4 • x 6 x • x 4 • x 3. WARM UP. 3. PRODUCT OF POWERS Write the expression as a single power of the base (LESSON 8.1). x 2 • x 5 (-5) • (-5) 8

ayanna-russell
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WARM UP

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  1. WARM UP 4 PRODUCT OF POWERS Write the expression as a single power of the base (LESSON 8.1). x2 • x5 (-5) • (-5)8 x2 • x4• x6 x • x4 • x3

  2. WARM UP 3 PRODUCT OF POWERS Write the expression as a single power of the base (LESSON 8.1). x2 • x5 (-5) • (-5)8 x2 • x4 • x6 x • x4 • x3

  3. WARM UP 2 PRODUCT OF POWERS Write the expression as a single power of the base (LESSON 8.1). x2 • x5 (-5) • (-5)8 x2 • x4 • x6 x • x4 • x3

  4. WARM UP 1 PRODUCT OF POWERS Write the expression as a single power of the base (LESSON 8.1). x2 • x5 (-5) • (-5)8 x2 • x4 • x6 x • x4 • x3

  5. WARM UP 0 PRODUCT OF POWERS Write the expression as a single power of the base (LESSON 8.1). x2 • x5 (-5) • (-5)8 x2 • x4 • x6 x • x4 • x3

  6. 9.5 Solving Quadratic Equations by Graphing GOAL Use a graph to find or check a solution of a quadratic equation KEY WORDS X-intercept Roots of a Quadratic Equation

  7. 9.5 Solving Quadratic Equations by Graphing The x-intercepts of graphy = ax2 + bx + c are the solutions of the related equations ax2 + bx + c = 0. Recall that an x-intercept is the x-coordinate of a point where a graph crosses the x-axis. At this point, y = 0.

  8. EXAMPLE 1 Use a Graph to Solve an Equation The graph of y = x2 – 8 is shown a the right. Use the graph to estimate the solutions of x2 – 8 = 0. SOLUTION The graph appears to intersect the x-axis at (-4, 0) and (4, 0). By substituting x = -4 and x = 4 in x2 – 8 = 0, you can check that -4 and 4 are solutions of the given equation. 9.5 Solving Quadratic Equations by Graphing

  9. 9.5 Solving Quadratic Equations by Graphing Checkpoint Use a Graph to Solve and Equation. The graph o f y = 2x2 – 4x is shown. Use the graph to estimate the solutions of 2x2 – 4x = 0. Check your solutions algebraically by substituting each one for x in the given equation.

  10. 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.

  11. EXAMPLE 2 Graph Quadratic Function with Positive a-Value Sketch the graph of x2 - x = 2 SOLUTION STEP 1 Write the equation in the standard form. x2 – x = 2 ORIGINAL EQUATION x2 – x – 2 = 0 SUBTRACT 2 FROM EACH SIDE. 9.5 Solving Quadratic Equations by Graphing

  12. EXAMPLE 2 Graph Quadratic Function with Positive a-Value Sketch the graph of y = x2 - x = 2 SOLUTION STEP 2Sketch the graph of the related function y = x2 – x – 2 . 9.5 Solving Quadratic Equations by Graphing y = x2 – x - 2

  13. EXAMPLE 2 Graph Quadratic Function with Positive a-Value Sketch the graph of y = x2 - x = 2 SOLUTION STEP 3 Estimate the values of the x-intercepts. The x-intercepts appear to be -1 and 2. 9.5 Solving Quadratic Equations by Graphing (-1, 0) (2, 0) x-intercept y = x2 – x - 2 x-intercept

  14. EXAMPLE 2 Graph Quadratic Function with Positive a-Value Sketch the graph of y = x2 - x = 2 CHECK YOUR ANSWER BY SUBSTITUING (-1)2 – (-1) – 2 = 0 ? (2)2 – (2) – 2 = 0 ? 9.5 Solving Quadratic Equations by Graphing (-1, 0) (2, 0) x-intercept y = x2 – x - 2 x-intercept

  15. 9.4 Graphing Quadratic Functions Checkpoint Solve an Equation by Graphing Use a graph to estimate the solutions of x2 + 2 = 6 Check your solutions algebraically.

  16. 9.4 Graphing Quadratic Functions (2, 0) Solve an Equation by Graphing 1. x2 + 2x = 3 (-1, 0) x-intercept y = x2 – x - 2 x-intercept

  17. 9.4 Graphing Quadratic Functions Solve an Equation by Graphing 2. -4x2 -8x = -12

  18. 9.4 Graphing Quadratic Functions Solve an Equation by Graphing 3. -x2 + 3x = -4

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