Linear Equations
What is the rate of change of with coordinates (-3, 2) and (-1, -6)
The rate of change is -4
What are the zeros of 2x2-6x-20?
[-2,5] pr (-2,0), (5,0)
Is y=3(1.23)x growing or decaying?
Growing
When you type this equation into DESMOS, 3q+7=2q
What change needs to be made so DESMOS can understand it?
Type x instead of q.
Simplify these terms:
(5x+6y)+(3x-2y)
8x+4y
What is the solution to 3x+2=2x-1
The solution is -3
Name the three other words that will often be used as synonyms for the x-intercepts of a function.
Zeros, solutions, and roots
Write an exponential equation that is decaying.
Any exponential equation with a positive nuber less than 1 as the exponent base.
Examples: y=0.09x or f(x)=1828(0.999)x
When you type this equation into DESMOS, 3q+7= 127
When I type this into DESMOS to solve it, what should go in front of the 127?
a y= should go in front.
Example: y=127
Evaluate f(5) given f(x)=2x+3
13
What is the slope and y-intercept of the following function?
-2y=8x-4
Slope: -4
Y-intercept: 2
What is the axis of symmetry of x2-6x-20?
x=3
Simplify this expression to one variable and one exponent.
(2m4)(5m7)
10m11
When you type this equation into DESMOS, 3x+7=2x
To solve this with DESMOS, where should the equation be split into two separate lines?
AND will the solution be the x value or the y value?
It should be split at the equal sign.
The solution will be the x-value.
Write the equation of any horizontal line.
y= (any constant)
Example: y=10 or y=-2
What is the y-value of the solution of the following system?
y=3x+5
6x+2y=30
8
Which of the following is a factor of 10x2-19x+6?
A. 10x-3
B. 10x-1
C. 5x-3
D. 5x-2
D. 5x-2
Write the equation if there is a y-intercept of 10 and exponential growth of 23%.
y=10(1.23)x
You see the word equivalent in a problem. You type the equation in the question and all of the answer choices into desmos. How will you know which is the correct answer?
Whichever answer choice is the exact same line as the original equation.
What is the range of y=(x-2)2+3?
The range is all real numbers greater than or equal to 3. You could also write this as an inequality.
Describe the following inequality below by picking dashed/solid and shaded above/below.
-5y>15x+10
Shaded below and dashed
Write the equation of a quadratic that is the parent function y=x2 shifted up 3 and right 4
y=(x-4)2+3
Simplify this expression:
(3q2p4)(6q7p)
3q9p5
Rearrange this equation so DESMOS will understand it:
14x-7y=35
y=2x-5 or
y=-14x+35 with a -7 underneath EVERYTHING on the right side of the equation
(sorry jepoardy won't let me type out the second possible equation)
Ms. Pokala gathers her change to buy food. She has 18 nickels and quarters that total $2.30. Write a system of equations that represents this scenario.
x=nickels y=dimes
x+y=18
0.05x+0.1y=2.30