![]() 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. Looking at the system, it can be noted that both equations of the system are written in standard form. You can improve your estimate by zooming in. To solve a quadratic-quadratic system graphically, both quadratic equations are graphed to identify the points of intersection. ![]() 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. These Quadratic Functions Worksheets are a good resource for students in the 5th Grade through the 8th Grade.\) You may select the difficulty of the problems you want to use. These Algebra 1 - Quadratic Functions Worksheets produces problems for solving quadratic equations by completing the square. Solving Quadratic Equations by Completing the Square Worksheets These Quadratic Functions Worksheets are a good resource for students in the 5th Grade through the 8th Grade. These Algebra 1 - Quadratic Functions Worksheets produces problems for solving quadratic equations with the quadratic formula. Solving Quadratic Equations With the Quadratic Formula These Algebra 1 - Quadratic Functions Worksheets produces problems for solving quadratic equations by factoring. Solving Quadratic Equations by Factoring Worksheets These Algebra 1 - Quadratic Functions Worksheets produces problems for solving quadratic equations by taking the square root. You may select what type of "b" term you want to use. ![]() These Algebra 1 - Quadratic Functions Worksheets produces problems for completing the square. You can select the magnitude of the "a" term and the direction in which the parabola opens. This Algebra 1 - Quadratic Functions Worksheet produces problems for graphing quadratic inequalities. Graphing Quadratic Inequalities Worksheets ![]() This Algebra 1 - Quadratic Functions Worksheets will produce problems for practicing graphing quadratic function from their equations. Detailed Description for All Quadratic Functions Worksheets
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