5 part ii using given information about the graph to

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Part II. Using given information about the graph to find the quadratic equation. 2. There are different algebraic ways to find a reasonable quadratic model of the situation. We have some information about the path of the ball, giving some information about points of its graph (a parabola). Suppose the ball was 4.56 feet above ground when Ernie Thayer hit it, and that it reached a maximum height of approximately 108.42 feet when it was approximately 202.6 feet away from where he hit the ball. The ball lands after travelling a ground distance of approximately 409.6 feet . We will find equations to model the situation by using two algebraic meth- ods. ( Show all your work for each part. ) (a) Find an equation of the form y = C ( x - z 1 )( x - z 2 ) where z 1 and z 2 are the zeros (or roots) of the quadratic polynomial (or x -intercepts of the graph) and C is a scaling constant that needs to be determined. i. Find the other root. ( Hint: Use the known root, the vertex, and a symmetry property of the graph.) ii. Find the constant C . ( Round this value to three significant posi- tions. Leading zeros are not significant, but trailing zeros are signif- icant. For example, 0.0003478 would be rounded to 0.000348 and 0.0003501 would be rounded to 0.000350. Hint: To find C , you can use the initial height.) iii. Write out the equation that you found and algebraically check that it satisfies all the necessary conditions. ( Note: Show your work! Expect small errors because of rounding.) (b) Find an equation of the form y = A ( x - h ) 2 + k where the vertex is at ( h , k ) and the constant A is a scaling factor. i. Based on the information that you were given, what are the coordi- nates of the vertex. ii. Find the constant A . ( Round this value to three significant positions .) iii. Write out the equation that you found and algebraically check that it satisfies all the necessary conditions. ( Note: Show your work! Expect small errors because of rounding.) 6
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Part III. Discussion of when algebra can be used to find a quadratic equation. 3. In part II, we used two different methods to find a quadratic equation to model the situation. Each required different information about the graph. (a) Can you use algebra to find a quadratic equation if you know the coor- dinates of just one point on its graph? (b) Can you use algebra to find a quadratic equation if you know the co- ordinates of just two points on its graph? If so, what information is needed?
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