Unit 4– Quadratic Formula, Systems of Equations, and Higher-Degree Polynomials
Research Artifact Question Options
DUE DATE: Friday, 1/9/2015
This task addresses one or more of the NYS Standards for Algebra 2/ Trigonometry:
A2.A.2
A2.A.3 A2.A.4 A2.A.16 A2.A.17 A2.A.20
A2.A.21
A2.A.23 A2.A.24
A2.A.25 A2.A.26
Directions: First, pick ONE (1) Research Artifact Question. Then, answer all parts
under that question. Finally, cite ALL sources that you used to help with your research
Research Artifact Question Option #1:
1. How can you find out if a quadratic equation has only one solution without solving the
equation?
2. How many solutions does y = 5x2 - 10x +5 have? Explain.
3. Write a quadratic equation with no real solutions. How do you know? Write a quadratic
equation that has two solutions. How do you know?
4. How can you use the discriminant to write an equation that has one solution? Write one.
5. Explain how to use a graph to find the number of solutions to a quadratic equation. Use a
graph to find the number of solutions to any quadratic equation. Include the graph with your
solution
6. Use the discriminant to predict the number and type of solutions of this equation:
9x2 +6x = -1. Then, use a graphing calculator to check your solution. Describe how the graph
verifies your answer.
Research Artifact Question Option #2:
1. Explain why you must check solutions of a rational equation back into the original equation.
2. Write a rational equation which has one solution: x = −3. Show your work.
3. Write a rational equation where you calculate three solutions, but then eliminate one after
checking your solution. Show your work.
4. When you divide a fraction by a fraction, you can flip the fraction in the denominator and
multiply it by the fraction in the numerator. Explain why this works with both words and
mathematical examples.
Research Artifact Question Option #3:
1. Explain how to use the quadratic formula to solve a quadratic equation. Include an example.
2. Write the keystrokes you use to find one solution of
using the quadratic
formula and a calculator. (Plug into the quadratic formula. Write out the calculator buttons you
push to calculate.) Is the solution rational or irrational? What does it mean to be rational or
irrational?
3. Suppose you cannot factor
about b?
into the product of two binomials. What can you say
4. a. Write two different quadratic equations which have the solutions
b. Find the product and sum of the roots from 4. a. (
) by first adding the roots (for
sum) and multiplying the roots for the product, then using the product and sum formulas. Why
do these formulas work?
Research Artifact Question Option #4:
1. Make up your own quadratic equation. Solve it by completing the square.
2. Write a quadratic equation that has only one solution and can be easily solved by completing
the square.
3. How can completing the square help write a quadratic equation in vertex form, which is
f (x) = a(x - h)2 + k?
4. Make up a quadratic equation: Solve it by factoring, Completing the Square, and by Using the
Quadratic Formula.
5. Make up another quadratic equation where it cannot be factored. Solve it by both Completing the
Square and by using the Quadratic formula.
6. Decide: What situations is Completing the Square easier? What situations is using the quadratic
formula easier? What situation is factoring easier? Show examples of each.