We know this even before plotting "y" because the coefficient of the first term, 10 , is positive (greater than zero).Įach parabola has a vertical line of symmetry that passes through its vertex. Our parabola opens up and accordingly has a lowest point (AKA absolute minimum). Parabolas have a highest or a lowest point called the Vertex. Step 4 : Equations which are never true :Ī a non-zero constant never equals zero. Observation : No two such factors can be found !!Ĭonclusion : Trinomial can not be factored Equation at the end of step 3 : 10 Step-2 : Find two factors of -700 whose sum equals the coefficient of the middle term, which is -7.įor tidiness, printing of 12 lines which failed to find two such factors, was suppressed Step-1 : Multiply the coefficient of the first term by the constant 10 The middle term is, -7x its coefficient is -7. The first term is, 10x 2 its coefficient is 10. Trying to factor by splitting the middle term Step 2 : Step 3 : Pulling out like terms :ġ00x 2 - 70x - 700 = 10 3.Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :ġ00*x^2-70*x-(700)=0 Step by step solution : Step 1 : Equation at the end of step 1 : ((2 2 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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