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Graphing Quadratic Equations

Please help with graphing quadratic equations and applications of quadratic equations.

Graph the equation.
Complete the table, answer the problem. And describe the resulting graphs by identifying the vertex point, the graph's direction, and any axis intercepts gleaned from the table or graph.
Identify the axis of symmetry, crate a suitable table of value, and sketch the graph

6. Find the x-intercepts

Solve each of the following applications. Give all answers to the nearest thousandth

7. The length of a rectangle is 1 cm longer than its width. If the diagonal of the rectangle is 4 cm, what are the dimensions (the length and the width) of the rectangle?

8. The equation gives the height of an arrow, shot upward from the ground with an initial velocity of 112 ft/s, where t is the time after the arrow leaves the ground. Find the time it takes for the arrow to reach a height of 180ft.

9. A ball is thrown upward from the roof of a building 100m tall with an initial velocity of 20m/s. Use this information for exercises to solve this problem.

When will the ball reach a height of 80m?

10. The demand equation for a certain type of printer is given by

The supply equation is predicted to be

Find the equilibrium price.


Solution Preview

Please see the attached file.
Book1.xls is the excel file for problem 1.
Book2.xls is the excel file for problem 4.

Graph the equation.

First find the vertex of the parabola,

So the vertex is (2, -4).
Now we need to select several points on both sides of x = 2 and find out y values.
x y
-2 12
-1 5
0 0
1 -3
2 -4
3 -3
4 0
5 5
6 12

Finally connect the points via a smoothing curve.
In excel, Insert-> chart-> scatter plot

It is a straight line equation. We only need two points to graph a line. Usually, we use x- and y- intercepts.
x-intercept: y = 0, -x + 1 = 0, x = 1, (1, 0)
y-intercept: x = 0, y = 0 + 1 = 1, (0, 1)
then connect the two points using a straight line.

x-intercept: (-1, 0)
y-intercept: (0, 1)

The vertex is (0, 0).
Then we complete the following ...

Solution Summary

Quadratic equations are graphed and solved. The solution is detailed and well presented.