2.1- Solving Equations Graphically

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Presentation transcript:

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 How could you change the first equation to get to the second?

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:

The x-intercept Method

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

Making Things Easier: Technological Quirks

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

Example 1: Solving a Quadratic Equation by Factoring

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

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

The Quadratic Formula: Our Friend

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