![]() ![]() 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. Solving a quadratic equation means finding the x-values that will make the quadratic function equal zero in other words, it means finding the points where the graph of the function crosses the x-axis. 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. And we can do more complicated functions, like: f (x) x². The input is simply the x I chose (in this case 2) and the output was what the function spat out (in this case, 4). 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. That means that, when we input any x into f (x), our answer is going to be 2 times that x. 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. You will also practice solving real-world problems using graphs. You will explore how to find the intercepts, axis of symmetry, and vertex of a quadratic function using technology. The approximate value of the roots will be shown on the screen. Learn how to solve quadratic equations by graphing with this interactive lesson. 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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