Quadratics
Find the solutions to the following quadratic equation:
(x-5)(x+9)=0
x = 5 and x = -9
Algebra: Is this a function: {(1, 2), (-2, 3), (2, 4)}
Yes, the domain does not repeat.
Algebra: What is the slope-intercept of a linear equation perpendicular to y = 2/3x+9
-3/2
Julia traveled to Argentina and Chile for a total of 16 days. In Argentina, she learned 125 new words per day. In Chile, she learned 140 new words per day. She learned a total of 2145 words. Write a system of equations using x for Argentina and y for Chile.
x + y = 16
125x + 140y = 2145
Gerry buys a car for $12,000. It depreciates at a rate of 8% per year. Write an equation to find the cost of the car after x years.
y = 12000(0.92)x
y = 12000(1-0.08)x
Solve the equation:
|x|-5=7
x = 12 and x = -12
The domain of exponential functions is always ____________ unless specified by a real-world problem.
All Real Numbers
Find the roots to the quadratic equation:
2x2=200
x = 10 and x = -10
Algebra: simplify: 4(6ac - 3) + 5ac
Algebra: 29ac-12
Write the following equation in slope-intercept form: 6(x + 3y) = 12
y = -1/3+2/3
Solve the following system of equations:
6x − 12y = 24
−x − 6y = 4
(2, -1)
Simplify (45)2
410
Solve the equation.
2|x-5| = 12
x = 11 or x = -1
In this exponential equation, what do EACH of the numbers stand for?
f(x) = 3(2)x
3 - y-intercept or start value
2 - growth factor or multiplier
What are the a, b, and c values in this equation?
2m2 + 2m − 12 = 0
a=2
b=2
c=-12
Algebra: Solve for a: abc + 2h
Algebra: a = -2h/bc
Write an equation in point-slope form with a slope of 1/5 and passes through the point (2, -6).
y + 6 = 1/5 (x - 2)
Solve the following system of equations:
x + 7y = 0
2x − 8y = 22
(7, -1)
Factor the following polynomial.
x2 -5x - 24
(x-8)(x+3)
Solve:
4|x+3|-11=5
x = 1 or x = -7
{1,-7}
What is an asymptote?
an imaginary line that exponential graphs approach but never actually touch....used in the range.
Find the solution(s) to the following quadratic:
x2 +8x +16 = 0
x = -4
Simplify: a(b - c) - 2a(c + b)
-1ab - 3ac
Write an equation parallel to the equation y = 2x+3 and goes through the point (-8, 1) in slope-intercept form.
y = 2x+17
Solve the following system of equations:
−8x − 10y = 24
6x + 5y = 2
(7, -8)
Find the product of (x - 2)(x2 + 3x -4)
x3 + x2 - 10x +8
Solve the equation.
-3|x-1|+5=8
No Solution.
Does this exponential function representing growth or decay? How do you know?
f(x) = 2(0.4)x
Decay, factor is between 0 and 1.
A water balloon is catapulted into the air so that its height h, in meters, after t seconds is
h = -4.9t2 + 24.5t + 1. What is the maximum height of the balloon? Round to the nearest tenth.
h = 31.6 meters
Algebra: What's the domain of a exponential function?
All Real Numbers
Write an equation perpendicular to y = -0.25x + 3 and goes through the point (5, -2) in slope-intercept form.
y = 4x-22
If two lines intersect, then the solution to the system is:
a. One solution
b. Infinitely Many Solutions
c. No solution
One solution
Factor the following polynomial.
25x2-64
(5x+8)(5x-8)
Solve the equation.
0.8|x+4|-3=1
x = -9 or x = 1
In the function y= 2500(1.25)x, what is the start value of his investment? What percentage is it growing by?
2500 start value
25%