Quadratic Equation Application Problems
1.) Chrissy is planting a small vegetable garden next to a building. She has 12 feet of fencing to keep the animals out. What are the dimensions of the largest rectangle she can enclose if she uses the building for one side of the rectangle?
2.) C3PO has installed an ejection seat in his land rover for quick escapes. R2D2 is sky high after accidentally bumping the ejection switch. The seat throws R2 upward as described by y = 4 + 100x – 16x2 where x is the number of seconds after the ejection button is hit and y is the number of feet up after x seconds.
a.) How long before R2 is 88 feet above ground?
b.) How long before R2 is 170 feet above ground?
c.) How high is R2 after 6 seconds?
d.) When will R2 be at his highest?
e.) How high will he be?
f.) When will R2 hit the ground?
3.) For what values of c does the equation 2x2 - 5x + c = 0 give 2 real solutions.
4.) Give an equation of a parabola which has the x-intercepts (-2,0) and (1,0).
5.) Write a quadratic equation whose solutions are: x = 2 and x = -4.
6.) The outside measurements of a rectangular picture frame are 14 inches by 16 inches. The frame has the same width all around and the picture area is 48 square inches. How wide is the frame?
7.) Match the equations to their graphs below. Choose the best answer. Assume the scale on each graph is the same.
(i.) _____ y = -4x2- 2 (ii.) _____ y = 4x2 + 2
(iii.) _____
(iv.) _____
Answers:
1.) 6’ by 3’
2.) (a.) 1 sec & 5.25 sec. (b.) never (c.)
28’ (d.) 3.125 sec (e.) 160.25 ft
(f.) 6.29 sec
3.) c < 25/8
4.) many ans.: y = x2 + x - 2
5.) many ans.: 0 = x2 + 2x - 8
6.) w = 4 inches
7.) (i) f (ii) b (iii) a (iv) g
