1. Find the coordinates of the vertex for the parabola defined and give the domain of the function in set-builder notation:
f(x) = −3(x + 2)2 + 12
2. Use the vertex and intercepts to graph the quadratic function. Give the equation of the parabola’s axis of symmetry. Use the graph to determine the Domain and Range of the function (also in set-builder notation):
y − 3 = (x − 1)2
3. Use the vertex and intercepts to graph the quadratic function. Give the equation of the parabola’s axis of symmetry. Use the graph to determine the Domain and Range of the function (also in set-builder notation):
g(x) = 2x2 − 7x − 4
4. Determine, without graphing and the use of a calculator, whether the function has a Minimum value or a Maximum value. Find the Minimum or Maximum value and determine where it occurs for:
h(x) = −2x2 − 12x + 3
5. Give the domain and range in set-builder notation for the given quadratic function whose graph is described:
• the vertex is (−3, −4)
• and the parabola opens down.
6. Give the domain and range in set-builder notation for the given quadratic function whose graph is described:
. the minimum = 18 at x = 10
7. (*) Write an equation, in standard form, of the parabolic function that has the shape as the graph of f(x) = 2x2, but with the vertex as the given point: (-8, -6)
8. Determine whether f(x) = α4 - 2α2 + 1 is even, odd, or neither. Describe the symmetry, if any, for the graph of f.
9. An athlete whose event is the shot-put releases the shot with the SAME initial velocity, but at different angles (35°, 65°) is based on parabolic functions that model parabolic paths. When the shot whose path is released at an angle of 65°, its height, g(x), in feet, can be modeled by:
g(x) = —0.04x2 + 2.1x + 6.1
where x is the shot’s horizontal distance, in feet, from its point of release. Use this model to solve the following:
(a) What is the maximum height, to the nearest tenth of a foot, of the shot and how far from its point of release does this occur?
(b) What is the shot’s maximum horizontal distance, to the nearest tenth of a foot, or the distance of the throw?
(c) from what height was the shot released?
10. You have 200 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river, find the length and width of the plot that will maximize the area. What is the largest area that can be enclosed?
11. Does the following make sense? State Yes, or No, and why you believe it to be so (This is NOT a guessing question, you need to support your argument here):
The graph of h(x) = -2(x + 4)2 -8 has one y-intercept and two x-intercepts.
12. Given f(x) =4 5 - (x - 1 2)2, find the following information and graph on a rectangular coordinate system:
13. Given y = 0.01x2 + 0.6x + 100, find the following information and graph on a rectangular coordinate system:
14. Find the A.O.S. for the given parabolic curve whose equations is given below. Use the A.O.S. to find a second point on the parabola whose y-coordinate is the same as the point given:
h(x) = (x - 3)2 + 2
with point: (6,11)
15. Solve by factoring: 4x2 - 13x = -3
16. Solve using the square root property: 2x2 - 7 = -15
17. Solve using the square root property: (2x + 8)2 = 27
18. Determine the constant that should be added to the binomial so that is becomes a perfect square trinomial. Then Factor the trinomial:
β2 + 4 5β
19. Solve using C.T.S. (Completing the Square): 3 7x2 - 2 9x = 3 1
20. Solve using C.T.S.: 2α2 - 3α - 5 = 0
21. Calculate the Discriminant. Then determine the number and type of solutions for the given function:
2x2 + 11x - 6 = 0
22. Solve using any method you choose (Not with a calculator!): 1 1 1
x + x + 3 4
23. Solve using any method you choose (Not with a calculator!):
24. The base of a 57 foot ladder is 17 feet from a building. If the ladder reaches the flat roof, how tall is the building?
25. Each side of a square is lengthened by 2 inches. The area of the new, larger square is 36 square inches. Find the length of a side of the original square.