9. The height of a baseball in feet tossed upward is given by the function

where

*t*represents time in seconds. What is the maximum height of the baseball?
10. Find a quadratic equation with solutions: {±5

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*i*}
Showing posts with label **parabola**. Show all posts

Showing posts with label **parabola**. Show all posts

Click on the 10 question exam covering topics in chapter 6. Give yourself one hour to try all of the problems and then come back and check your answers.

9. The height of a baseball in feet tossed upward is given by the function

where *t* represents time in seconds. What is the maximum height of the baseball?

10. Find a quadratic equation with solutions: {±5*i*}

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At this point in our study we should be able to find

One of our basic functions

can be graphed by plotting points. We do this by choosing about five

The more points we plot the easier it is to see that the graph is u-shaped. The *vertex*, in this case, is the point where the graph changes from decreasing to increasing, or the point with the smallest *y*-value. Here the vertex is (0, 0) which is also the *x*- and *y*-intercept. The line *x* = 0, the *y*-axis, is the *line of symmetry*. This is the line where we could fold our paper to see that the two sides of the graph coincide.

Line of symmetry: *x* = 1

x-intercepts: (-2,0) and (4,0)

y-intercept: (0, -8)

Vertex: (1, -9)

5th point: (2, -8)

Recall that two points determine a line - this is not the case for parabolas. Parabolas require a minimum of 3 points but we usually want to find at least five points to make a nice graph. Find the vertex,

The domain and range of the above function can be determined by the graph. In the previous problem the domain consists of all real numbers and the range consists of all real numbers greater than or equal to −1. Also, it is useful to note that we have a minimum

When trying to find

This parabola looks a bit different, notice that it opens down and also notice that the previous parabola opened up. There is an easy test to know which way it opens even before we begin.

Therefore, when asked to graph a parabola, you can get two important pieces of information without doing any work. By inspection you can tell if it opens up or down and you can identify

Please keep in mind that all quadratic functions have a vertex and a

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