Zeros
Determine the zeros of the function: y = 2x2 + 5x - 3
x = 1/2
x = -3
Solve: -x2 + 4 is greater than zero
( -2, 2)
Solve: 1/64 = 2x-1
x = -5
The table shows the time t in seconds required for a car to attain a speed of s miles per hour from a standing start.
Speed, s = 30, 40, 50, 60, 70, 80, 90
Time, t = 3.4, 5.0, 7.0, 9.3, 12.0, 15.8, 20.0
Determine the seconds required to hit 65 mph.
t = 10.22 secs.
Solve: 2x + 3y - 4z = -5
-x - 2y + z = 1
-4x + y + 2z = -9
(3, -1, 2)
Determine the possibilities for zeros:
y = 2x4 - 3x3 + x2 - x + 10
possibilities: +/- 2, +/- 1, +/-5, +/-10, +/-1/2, +/-5/2
Approximate where f(x) = g(x)
f(x) = 2x - 1 g(x) = x2 - 8
x = 3.828
x = -1.828
Solve. Give an exact answer.
52x-1 = 2-3x+4
x = (ln 16 + ln 5) / (ln 25 + ln 8)
Use an augmented matrix to solve the systems of linear equations:
3x - 2y + z = 15
-x + y + 2z = -10
x - y - 4z = 14
(5, -1, 2)
Solve for X. 2X - A = B
A = [ 1 2 -1 B = [ 5 -6 1
3 1 -2 -2 3 -4
-1 4 -5] -3 8 -9]
X = [ 3 -2 0
1 2 -3
-2 6 -7]
Determine the zeros: y = 4x3 - 5x
x = 0, x = +/- sqrt 5/2
Determine where the function is increasing, decreasing, or constant.
y = (1/2)x3 - 5x
Increasing: (-infinity, -1.826) U (1.826, infinity)
Decreasing: (-1.826, 1.826)
Solve: log2 x + log2(x + 4) = 5
x = 4
How many years will it take to double an investment of $5000 with an interest rate of 6.5% compounded monthly?
10.7 years
Multiply A times B.
A = [ 2 4 -3] B = [ -6 0 2
5 1 -4
-2 -1 8]
AB = [14 7 -36]
Approximate where f(x) is greater than or equal to g(x).
f(x) = x2 - 5x + 6 g(x) = 2x - 3
(- infinity, 1.697]
[ 5.303 , infinity)
Where does f(x) exceed g(x)?
f(x) = 3x2 - 5x - 9
g(x) = x - 1
(-infinity, -0.915) U (2.915, infinity)
If x is a real number and resides between 0 and 1, compare:
A. 1/x2 B. 1/x3
B is greater than A.
Margaret ordered 200 flowers for the church for Mother's Day. In the mix were carnations at $1.50, roses for $5.75, and daisies for $2.60 each. The total rang up at $589.50. She did get 20 fewer roses than daisies.
How many of each flower did she order?
Carnations = 80
Roses = 50
Daisies = 70
Multiply C x D
C = [-3 0 2 D = [-2 6
1 3 -2 3 -4
5 -1 4] 2 1]
CD = [10 -16
3 -8
-5 38]
Graph the following function, include zeros, intercept(s), asymptotes.
y = [(x-3)(x+2)(x+5)]/[(x+1)(x-2)]
[Graph]
Where does g(x) exceed f(x)?
f(x) = 2x - 3
g(x) = x3 - 4x2 + 5
(-1.414, 1.414) U (4, infinity)
Solve. Give an exact answer.
log224 = x
x = 3 + log23
Max had $24,500 to invest in three different accounts. The first paid 4% interest, the second paid 5.5% interest, and the third paid 6%. At the end of the year, he had made $1300. If the amount of money in the lowest paying account was four times the amount in the middle account, how much money was in each account?
$8000 in the 4% account
$2000 in the 5.5% account
$14,500 in the 6% account
Find the equation of the parabola y = ax2 + bx + c passing through the points (-3, 13), (0, -4),
and (3, -1).
y = 10/9x2 - 7/3x + 4