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Quadratic functions

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1) Solve 6x2 + 3x - 18 = 0 using the quadratic formula.
Read the information in the assignment list to learn more about how to type math symbols, such as the square root.

2) Use the graph of y = x2 + 4x - 5 to answer the following:

a) Without solving the equation, use the graph to determine the solution(s) to the equation?

b) Does this function have a maximum or a minimum?

c) What are the coordinates of the vertex in (x, y) form?

d) What is the equation of the line of symmetry for this graph?

3)
a) Calculate the value of the discriminant of .

b) By examining the sign of the discriminant in part a, how many x-intercepts would the graph of have? Why?

4) a) Find the corresponding y values for x = -4, -3, -2, -1, 0, 1, 2 if .

Answer (fill in y column)
x y
- 4
- 3
- 2
- 1
0
1
2

b) Use Microsoft Excel to plot the points found in part a and to sketch the graph.
Read the information in the assignment list to learn more about how to graph in MS Excel.

5) The path of a falling object is given by the function where represents the initial velocity in ft/sec and represents the initial height. The variable t is time in seconds, and s is the height of the object in feet.

a) If a rock is thrown upward with an initial velocity of 32 feet per second from the top of a 40-foot building, write the height equation using this information.

Typing hint: Type t-squared as t^2.

b) How high is the rock after 0.5 seconds?

c) After how many seconds will the rock reach maximum height?

d) What is the maximum height?

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Solution Summary

This solution consists of many problem that explain the concept of finding discriminant, finding roots and graphing quadratic functions. It also explains the concept of finding maximum nad minimum point of a quadratic function.

Solution provided by:
Sandhya Sharma, MSc
Education
  • BSc, Meerut University
  • MSc, Meerut University
  • MPhil, Institute of Advanced Studies
  • MSc, AIT
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