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Quadratic Equations

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See the attached file.
1. Use discriminant to determine whether the following equations have solutions that are: two different rational solutions; two different irrational solutions; exactly one rational solution; or two different imaginary solutions.
x^2 - 12x + 34 = 0

2. Use the quadratic formula to determine the x-intercepts (if any) of the following function. Then evaluate the function for several values of x, and use the resulting points to graph the function. Show your work and graph.
f(x) = x2 + 2

3. Answer the question. You will need to use the formula 4.9t^2 + vot = s.
Approximately how far will an object fall in 4 seconds, if it is thrown downward at an initial velocity of 20 meters per second (v0) from a helicopter?

4. Translate the problem into a pair of linear equations in two variables. Solve the equations using either elimination or substitution. State your answer for the specified variable.
Andy has 14 coins made up of quarters and half-dollars, and their total value is $4.25. How many quarters does he have?

5. Without graphing, find the maximum value.
f(x) = (x + 5)^2 - 5.

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This solution is comprised of detailed explanation and step-by-step calculation of the given quadratic equation problems and provides a clear perspective of the underlying concepts.

Solution provided by:
Anwesha Ghosh, MSc
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  • MSc, Osmania University
  • MSc, Indian Institute of Technology - Roorkee (I.I.T.-ROORKEE)
  • BSc, Banaras Hindu University
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