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2.1- Solving Equations Graphically

2.1- Solving Equations Graphically. Mathematical Language. A solution of an equation is a number that make the equation true 3x+2=17 To solve an equation means to find all its solution. Two equations are equivalent if they have the same solutions 3x+2=17 and x-2=3

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2.1- Solving Equations Graphically

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  1. 2.1- Solving Equations Graphically

  2. Mathematical Language • A solution of an equation is a number that make the equation true • 3x+2=17 • To solve an equation means to find all its solution • Two equations are equivalent if they have the same solutions • 3x+2=17 and x-2=3 • How could you change the first equation to get to the second?

  3. The Intersection Method We are trying to find a x that makes the left side equal to the right side Separate: Find a input, a x-value, that makes the two outputs, the y values, the same. This input will be the x-coordinate of the intersection point between the two graphs Check:

  4. The x-intercept Method

  5. Example 2: Solving an Equation by Using the x-Intercept Method

  6. Making Things Easier: Technological Quirks

  7. 2.2 Solving Quadratic Equations Algebraically Factoring Taking the square root of both sides of the equation Completing the square Using the quadratic formula

  8. Example 1: Solving a Quadratic Equation by Factoring

  9. Taking the Square Root of Both Sides of an Equation • Why do we do plus or minus • Think of an equation that would have no solutions

  10. Solving a Quadratic Equation by Completing the Square Notice no coefficient in front of x^2

  11. The Quadratic Formula: Our Friend

  12. 2.2 Hmwr: p. 1-11odd, 19-33odd, 47-55odd

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