MATH1050: Quadratic Polynomials
Instructor: Laura Strube
Name:
Student ID:
Answer the questions in the spaces provided or copy the questions neatly on
your own paper
1. (5 points) Given f (x) = 2x2 + 6x + 3, find the roots of f(x) by completing the square
and then solving f (x) = 0 for x.
Do not use the formulas in the text
1
2. (5 points) Now find the roots of f using the quadratic formula
3. (5 points) Answer the following questions about f and then graph on the attached graph
paper.
(a) What is the vertex of the parabola?
(b) What are the roots of the parabola?
(c) What is the y intercept of the parabola?
(d) At what y value does the parabola have width 2?
(e) At what y value does the parabola have width 4?
(f) Is the parabola opening up (concave up) or opening down (concave down)?
(g) Is the parabola stretched vertically, shrunk vertically, or neither?
4. (5 points) Given g(x) = 12 x2 + 4x + 4, find the roots of g by completing the square, and
then solving g(x) = 0 for x.
Do not use the formulas in the text
5. (5 points) Find the roots of g using the quadratic formula
6. (5 points) Answer the following questions about g and then graph on the attached graph
paper/
(a) What is the vertex of the parabola?
(b) What are the roots of the parabola?
(c) What is the y intercept of the parabola?
(d) At what y value does the parabola have width 2?
(e) At what y value does the parabola have width 4?
(f) Is the parabola opening up (concave up) or opening down (concave down)?
(g) Is the parabola stretched vertically, shrunk vertically, or neither?
7. (5 points) Given the function p(x) = ax2 + bx + c, complete the square. Your answer
should match the “completing the square” formula given in the text.
8. (5 points) Using the formula you found above (or the formula in the text), solve p(x) = 0
to find the roots of p. Your answer should match the “quadratic formula” given in the
text.