warm up product of powers write the expression as a single power of the base (lesson 8.1). 1.x 2 x 5...
Post on 17-Dec-2015
218 Views
Preview:
TRANSCRIPT
WARM UP
PRODUCT OF POWERS Write the expression as a single power of the base (LESSON 8.1).
1. x2 • x5
2. (-5) • (-5)8
3. x2 • x4 • x6
4. x • x4 • x3
4
WARM UP
PRODUCT OF POWERS Write the expression as a single power of the base (LESSON 8.1).
1. x2 • x5
2. (-5) • (-5)8
3. x2 • x4 • x6
4. x • x4 • x3
3
WARM UP
PRODUCT OF POWERS Write the expression as a single power of the base (LESSON 8.1).
1. x2 • x5
2. (-5) • (-5)8
3. x2 • x4 • x6
4. x • x4 • x3
2
WARM UP
PRODUCT OF POWERS Write the expression as a single power of the base (LESSON 8.1).
1. x2 • x5
2. (-5) • (-5)8
3. x2 • x4 • x6
4. x • x4 • x3
1
PRODUCT OF POWERS Write the expression as a single power of the base (LESSON 8.1).
1. x2 • x5
2. (-5) • (-5)8
3. x2 • x4 • x6
4. x • x4 • x3
WARM UP 0
GOAL•Use a graph to find or check a solution of a quadratic equationKEY WORDS•X-intercept•Roots of a Quadratic Equation
9.5 Solving Quadratic Equations by Graphing
The x-intercepts of graph y = 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.
9.5 Solving Quadratic Equations by Graphing
EXAMPLE 1 Use a Graph to Solve an EquationThe graph of y = x2 – 8 is shown a the right. Use the graph to estimate
the solutions of x2 – 8 = 0.
SOLUTIONThe graph appears to intersect the x-axis at (-4, 0) and (4, 0). By substituting x = -4and 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
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.
9.5 Solving Quadratic Equations by Graphing
ESTIMATING SOLUTIONS BY GRAPHINGThe 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 = 0STEP 2 Sketch the graph of the related quadratic functiony = 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
EXAMPLE 2 Graph Quadratic Function with Positive a-ValueSketch the graph of x2 - x = 2SOLUTIONSTEP 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
EXAMPLE 2 Graph Quadratic Function with Positive a-ValueSketch the graph of y = x2 - x = 2SOLUTIONSTEP 2 Sketch the graph of the related function y = x2 – x – 2 .
9.5 Solving Quadratic Equations by Graphing
y = x2 – x - 2
EXAMPLE 2 Graph Quadratic Function with Positive a-ValueSketch the graph of y = x2 - x = 2SOLUTIONSTEP 3 Estimate the values of the x-intercepts. The x-intercepts appear
to be -1 and 2.
9.5 Solving Quadratic Equations by Graphing
y = x2 – x - 2
(-1, 0) (2, 0)
x-intercept x-intercept
EXAMPLE 2 Graph Quadratic Function with Positive a-ValueSketch the graph of y = x2 - x = 2CHECK YOUR ANSWER BY SUBSTITUING(-1)2 – (-1) – 2 = 0 ? (2) 2 – (2) – 2 = 0 ?
9.5 Solving Quadratic Equations by Graphing
y = x2 – x - 2
(-1, 0) (2, 0)
x-intercept x-intercept
Checkpoint Solve an Equation by Graphing
1. Use a graph to estimate the solutions of x2 + 2 = 62. Check your solutionsalgebraically.
9.4 Graphing Quadratic Functions
x
y
Solve an Equation by Graphing
1. x2 + 2x = 3
9.4 Graphing Quadratic Functions
x
y
x-intercept
x-intercept
y = x2 – x - 2
top related