Solving Quadratic Equations by Graphing. Essential Question Where are the solutions to quadratic equations located on the graph of the parabola?

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Presentation transcript:

Solving Quadratic Equations by Graphing

Essential Question Where are the solutions to quadratic equations located on the graph of the parabola?

Steps for Solving Quadratics by Graphing: 1.Enter the equation into y= 2.Press GRAPH. 3.Press 2 nd TRACE (CALC) 4.Select 2: zero 5.Let’s focus on the left-most intercept: Using the arrows, arrow over to the left side of the intercept and press ENTER. 6.Arrow over to the right side of the intercept and press ENTER. 7.Press ENTER one more time when the calculator takes a guess. 8.Repeat this process for the right-most intercept (if there is one). TIPS: The calculator will ONLY give you a rounded solution!! 1) Does the graph cross the x-axis? If not, then you MUST use the Quadratic Formula to gain the solution. 2) Do you need an EXACT solution? If so, then use the Quadratic Formula if it is not factorable.

Practice: Find the solutions using a graph (Don’t forget to set the equation equal to zero first. Round any irrational solutions to two decimal places.) 1. 3x 2 – 5x – 1 = x 2 – 5x – 2 = 0 3. x 2 – 6x + 2 = x 2 – 5x – 1 = 7x 2 – 3x – 14

Reflection: Where are the solutions to an equation found (once it has been set equal to zero)? What buttons on the calculator do I need in order to find those solutions? Can I use a graph with a calculator to find the solution to a quadratic equation?