Linear Legends
In
y = mx + b,
which letter is slope and which is y-intercept?
m=slope, b=y-intercept
What does the crossing point of two lines represent?
The solution
Which variable goes on the x-axis?
Independent
Value of any number to the zero power?
1
(2x + 3) + (4x - 1)?
6x + 2
Any number to the power of 1?
Itself
(3x^2 + 5x) - (x^2 + 2x)?
2x^2 + 3x
3x - 7 = 11?
x=6
Parallel lines mean how many solutions?
No solution
In
ax^2 + bx + c,
which letter is the constant?
c
Axis for the dependent variable?
y-axis
If
f(x) = 10 - x,
find
f(3).
7
Slope of a horizontal line?
0
Equation with slope=5, y-int=-2?
y=5x-2
U-shaped graph of a quadratic?
Parabola
What type of correlation is it if both variables increase together?
Positive
If you get a statement like
5 = 5,
how many solutions?
Infinitely many
If
f(x) = 3x - 5,
find
f(4).
7
Simplify
x^3 \cdot x^5.
x^8
Multiply
(x + 2)(x + 3).
x^2 + 5x + 6
Simplify
(x^4)^2.
x^8
Multiply
(x + 4)(x - 4).
x^2 - 16
2(x+5) = 18?
x=4
y = 2x
and
x + y = 9?
(3, 6)
If the Discriminant is exactly zero, how many real solutions?
One
What is the Domain?
All x-values
Test for a function on a graph?
Vertical Line Test
Rate of change between
(2, 10)
and
(4, 20)?
5
y-intercept of
2x + 3y = 12?
4
y = 100(0.85)^x
growth or decay?
Decay
Slope through
(2, 3)
and
(4, 7)?
2
Best method if one equation is
y = 2x + 1?
Substitution
Is "number of people in a room" discrete or continuous?
Discrete
Rewrite
x^{-3}
with positive exponents.
1/x^3
Factor
x^2 - 9.
(x - 3)(x + 3)
5x^2 \cdot 3x^5?
15x^7
GCF of
12x^3
and
8x^2?
4x^2
Flip the sign when?
Multiplying/Dividing by a negative
Easiest variable to eliminate in
3x+4y=10
and
2x-4y=5?
y
Find the values of a, b, and c in the equation
2x^2 + 4x - 10 = 0.
a=2, b=4, c=-10
Unconnected dots on a graph?
Discrete
Constant rate of
4, 7, 10, 13...?
+3
Rate of change of
y = x^2?
Variable/Non-constant
Slope of
x = 5?
Undefined
SURPRISE!
YOU FOUND THE SECRET SPACE!
Convert
y - 3 = 2(x - 1)
to slope-intercept form.
y = 2x + 1
Solve
x + y = 10
and
x - y = 2
using elimination.
(6, 4)
Define Domain and Range.
Domain=Inputs/x, Range=Outputs/y
Is
y = 5 \cdot (2)^x
growth or decay?
Growth
What is the name of the expression
b^2 - 4ac
inside the formula?
The Discriminant
*DAILY DOUBLE
Rewrite
4x^{-2}
without negative exponents.
4/x^2
Factor
x^2 + 7x + 10.
(x+5)(x+2)
x/3 + 5 = 2?
x=-9
x + y = 12
and
x - y = 4?
(8, 4)
If
a=1, b=6, and c=9,
what is the value of the discriminant
(b^2 - 4ac)?
0
... because
36 - 36 = 0
Range of
y = x^2?
y \ge 0
Every input has exactly ___ output.
One
Perpendicular slope to
1/3?
-3
Point-slope form for
(1, 2)
and
m=4?
y-2 = 4(x-1)
If a graph touches the x-axis at
x=3
and
x=-3,
what are those points called?
x-intercepts, roots, or zeros
Find intercepts for
3x + 4y = 12.
x:(4, 0), y:(0, 3)
How do you find the solution to a system of inequalities on a graph?
Overlapping shading
Linear vs. Nonlinear rate of change?
Linear is constant; Nonlinear varies
Value of
16^{1/2}?
4
If the Discriminant is a negative number, how many times does the graph touch the x-axis?
Zero times / No real solutions
Simplify
(x^3/y^2)^4.
x^{12}/y^8
Expand
(2x - 3)^2.
4x^2 - 12x + 9
4x + 1 > 3x - 5?
x > -6
Infinitely many solutions means...?
It's the same line
If the Discriminant is a positive number, how many times does the parabola cross the x-axis?
Two times
Difference between highest and lowest value on an axis?
Scale/Range
If
g(x) = 2x^2,
find
g(-3).
18
Car goes 150 miles in 3 hours. Unit rate?
50 mph
Convert
y = 1/2x + 3
to Standard Form.
x - 2y = -6
*DAILY DOUBLE
Using the vertex form
y = (x-2)^2 + 5,
where is the lowest point of this parabola?
(2, 5)