Solving Quadratic Equations

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Presentation transcript:

Solving Quadratic Equations By Graphing

Vocab review Do you remember from unit 1? Zeros Zeros – the place where the graph crosses the x-axis A.K.A – x-intercepts or Roots or solutions

How many solutions does a Quadratic have? Sometimes is may have less than 2 solutions. Let’s see what that looks like. Two solutions because the highest exponent is 2

How many solutions does a Quadratic have? The graph crosses the x-axis twice 1 solution The graph crosses the x-axis once No solution The graph never crosses the x-axis

How many solutions does a Quadratic have? The graph crosses the x-axis twice 1 solution The graph crosses the x-axis once No solution The graph never crosses the x-axis

Your turn! How many solutions do each of these graphs have? 1. 2. 3. 1. 2. 3. 1 solution 2 solutions 2 solutions

Identifying the solutions from the graph X = -2, 2 X = -3 X = -4, 1

You try! Identify the solutions from the graph X = -2, 2 No solution

Writing the equation from the graph. Using the solutions from 2 slides ago X = -2, 2 X = -3 X = -4, 1 Y = (x + 3)2 Y = -(x + 4)(x – 1) Y = (x – 2)(x + 2)

You try! Write the equation of each graph. 1. 2. 3. Y = (x + 5)(x – 3) 1. 2. 3. Y = (x + 5)(x – 3) Y = (x + 4)(x – 1) Y = - (x – 4)2

Finding the solutions from a table Ex: 1 x 1 2 3 4 5 6 y -2 -1 This table is of a Quadratic with 2 two solutions Remember: The solution is also called a zero or x-intercept. Meaning that the y-coordinate of the solution is 0 These are my solutions X = 5, 3

Finding the sol’n from a table cont. Ex: 2 x -2 -1 1 2 3 Y 8 Find the solutions. X = -1 and 1

Finding the sol’n from a table cont. Ex: 3 x -2 -1 1 2 3 Y 16 9 4 Find the solutions. This problem only has one solution X = 2 Ex: 4 x -2 -1 1 2 3 Y 6 11 This problem no solution

Finding the sol’n from a table cont. Ex: 5 x -2 -1 1 2 3 Y 12 5 -3 -4 Find the solutions. This problem has two solution but only one is listed on the table X = 0 , 4

Finding the solutions from a graph There are zeros between -5 and -4 and between 1 and 2

Solutions from a table cont. Ex: 6 Find the interval where the zero is. x 1 2 3 4 5 6 y -2 -7 -3 The zeros are between 2 and 3 and between 5 and 6