MTH133
Unit 2 – Individual Project – A
Name:
1)Solve the following by factoring:
a)
Answer: x = -2, 8
Show your work here:
(x-8)(x+2) = 0
x-8 = 0, X = 8
x+2 = 0, X = -2
b)
Answer: 0, -7
Show your work here:
Factor out 6x:
6x(x+7) = 0
6x = 0, x = 0
X+7 = 0, x = -7
2)If , find
a)f(2)
Answer: -1
Show your work here:
2*2^2 – 4*2 – 1
8 – 8 – 1
-1
b)f(-1)
Answer: 5
Show your work here:
2*(-1)^2 – 4*-1 – 1
2 + 4 – 1
5
3)Solve 6x2 + 3x – 18 = 0 using the quadratic formula.
Read the information in the assignment list to learn more about how to type math symbols, such as the square root.
Answer: 3/2, -2
Show your work here:
X = (-3 ± sqrt(3^2 – 4*6*-18))/(2*6)
X = (-3 ± sqrt(9 + 432))/12
X = (-3 ± 21)/12
X = 18/12 or -24/12
X = 3/2 or -2
4)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, , using only the graph.
Answer: -5, 1
Explain how you obtained your answer(s) by looking at the graph:
The answers are located where the graph crosses the x axis.
b)Does this function have a maximum or a minimum?
Answer: Minimum
Explain how you obtained your answer by looking at the graph:
The vertex of the parabola is at the bottom (“minimum”) of the graph.
c)What are the coordinates of the vertex in (x,y) form?
Answer: (-2, -9)
d)What is the equation of the line of symmetry for this graph?
Answer: x=-2
5)
a) Calculate the value of the discriminant of.
Answer: 0
Show your work here:
D = b^2-4ac
= 4^2 – 4*1*4
= 16 – 16
= 0
b)By examining the sign of the discriminant in part a, how many x-intercepts would the graph of have? Why?
Answer: It would have exactly 1 x intercept. When the discriminant is 0, there is only one intercept.
6)a)Find the corresponding y values for x= -4,-3,-2,-1,0,1, 2 if.
Answer (fill in y column)
x / y- 4 / 5
- 3 / 0
- 2 / -3
- 1 / -4
0 / -3
1 / 0
2 / 5
Show your work here: (type x-squared as x^2 unless using a superscript feature).
(-4)^2 + 2*-4 -3 = 16 – 8 – 3 = 5
(-3)^2 + 2*-3 -3 = 9 – 6 – 3 = 0
(-2)^2 + 2*-2 -3 = 4 – 4 – 3 = -3
(-1)^2 + 2*-1 -3 = 1 – 2 – 3 = -4
(0)^2 + 2*0 -3 = -3
(1)^2 + 2*1 -3 = 1 + 2 – 3 = 0
(2)^2 + 2*2 -3 = 4 + 4 – 3 = 5
b) Use Microsoft Excel to plot the points found in part a and to sketch the graph.
Read the information in the assignment list to learn more about how to graph in MS Excel.
Graph:
7)The path of a falling object is given by the function where represents the initial velocity in ft/sec and represents the initial height. The variable t is time in seconds, and s is the height of the object in feet.
a)If a rock is thrown upward with an initial velocity of 32 feet per second from the top of a 40-foot building, write the height equation using this information.
Typing hint: Type t-squared as t^2.
Answer: s = -16t^2 + 32t + 40
b)How high is the rock after 0.5 seconds? Show all work.
Answer: 52 feet
Show your work here:
Plug in t = 0.5:
-16*0.5^2 + 32*0.5 + 40
-4 + 16 + 40
= 52
c)After how many seconds will the rock reach maximum height? Show all work.
Answer: 1 second
Show your work here:
The max will be at the vertex. The t coordinate is given by:
-b/2a
= -32/(2*-16)
= -32/-32
= 1
d)What is the maximum height? Show all work.
Answer: 56 feet
Show your work here:
Plug the 1 second back into the equation:
-16*1^2 + 32*1 + 40
= -16 + 32 + 40
= 56