0036Īnd when we are working on graphing these, we need to make sure that the quadratic equation is in this standard form. These are also sometimes called second-degree equations. 0016Īnd the reason a cannot equal 0 is that, if it did, this first term would drop out. OK, first to review: a quadratic equation has the standard form ax 2 + bx + c = 0, where a does not equal 0. I am going to introduce multiple methods for solving quadratic equations-some algebraically, 0006Īnd this first one is using graphing techniques that we have learned earlier. In today's lesson, we are going to talk about solving equations by graphing. Section 9: Exponential and Logarithmic Relations Solving Rational Equations and Inequalities Multiplying and Dividing Rational ExpressionsĪdding and Subtracting Rational Expressions Section 8: Rational Equations and Inequalities Solving Radical Equations and Inequalities Section 7: Radical Expressions and Inequalities Graphing and Solving Quadratic Inequalities Section 5: Quadratic Functions and InequalitiesĪnalyzing the Graphs of Quadratic Functions Solving Systems of Equations Using Matrices Solving Systems of Equations in Three Variables Solving Systems of Inequalities By Graphing Solving Systems of Equations Algebraically Section 3: Systems of Equations and Inequalities Section 2: Linear Relations and Functions Solving Compound and Absolute Value Inequalities 3.Algebra 2 Section 1: Equations and Inequalities Use your graphing calculator to solve Ex. Find how long it takes the ball to come back to the ground.Ģ2. The equation of the height of the ball with respect to time is \(y=-16 t^2+60 t\), where \(y\) is the height in feet and \(t\) is the time in seconds. Phillip throws a ball and it takes a parabolic path. How are the two equations related to each other?Ģ1. Graph the equations \(y=x^2-2 x+2\) and \(y=x^2-2 x+4\) on the same screen. What might be another equation with the same roots? Graph it and see.Ģ0. How are the two equations related to each other? (Hint: factor them.)Ĭ. What is the same about the graphs? What is different?ī. Graph the equations \(y=2 x^2-4 x+8\) and \(y=x^2-2 x+4\) on the same screen. Using your graphing calculator, find the roots and the vertex of each polynomial.ġ9. Whichever method you use, you should find that the vertex is at ( 10,−65).įind the solutions of the following equations by graphing.įind the roots of the following quadratic functions by graphing. The screen will show the x - and y-values of the vertex. Move the cursor close to the vertex and press. Move the cursor to the right of the vertex and press. Move the cursor to the left of the vertex and press. Use and use the option 'maximum' if the vertex is a maximum or 'minimum' if the vertex is a minimum. You can change the accuracy of the solution by setting the step size with the function. Use and scroll through the values until you find values the lowest or highest value of y. The approximate value of the roots will be shown on the screen. Use to scroll over the highest or lowest point on the graph. Whichever technique you use, you should get about x=1.9 and x=18 for the two roots. The screen will show the value of the root. Move the cursor close to the root and press. Move the cursor to the right of the same root and press. Move the cursor to the left of one of the roots and press Use and scroll through the values until you find values of y equal to zero. You can improve your estimate by zooming in. There are at least three ways to find the roots: For the graph shown here, the x-values should range from -10 to 30 and the y-values from -80 to 50. If this is not what you see, press the button to change the window size.
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