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College Algebra Term Paper
Solve the following quadratic equation by factoring:
A) X2 + 6x -16 = 0
(x-2) (x+8)= 0
(x+2) (x-8) = 0
x=-2, x-8
b) solve the quadratic equation 6x2 +3x-18 = 0 using the quadratic formula x= - b +/- ?(b2- 4ac)
+/- ?[32- (4*6*-18c)]
x = 3/2; x= 2
c) Compute the discriminant of the quadratic equation 2x2-3x - 5 = 0 and then write a brief sentence describing the number and type of solutions for the equation.
If x= - b +/- ?(b2- 4ac), then (b2- 4ac) is the discriminant b2- 4ac= -32- (4*2*-5) = 49
There are two solutions for the equation, 1 and 2 1/2, which one gets by plugging the discriminant into the quadratic formula and solving for x.
Use the graph of y=x2+4x-5 to answer the following:
a) Without solving the equation or factoring, determine the solution(s) to the equation, x^2 + 4x - 5 = 0, using only the graph. Answer: x= 0, x = -5. I obtained the answers by looking at the situation where y=0 and finding the value for x in those locations.
b) Does this function have a maximum or a minimum? The graph has a minimum, y= -9, because nothing on the graph goes below that point.
c) What are the coordinates of the vertex in (x, y) form?
(-2,-9)
See below to check:
x= - b +/- ?(b2- 4ac)
2a
y=x2+4x-5
h= -b/2a
h=-4/(2*1)= -2
k= 4ac-b2
4a
k= 4ac-b2 = (4*1*-5) - 42 = -20 -16 = -36/4 = -9
4a
4*1
4
d) What is the equation of the line of symmetry for this parabola? Answer: x= -2
3) The profit function for Wannamaker Trophies is P (x) = -0.4x2 + fx - m, where f represents the design fee for a customer's awards and…
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