Positive Lead coefficient & even degree = both ends going up
Positive Lead coefficient & odd degree = left end going down and right end going up
Negative Lead coefficient & odd degree = left end going up & right end going down
Negative Lead coefficient & even degree = both ends going down
Standard Quadratic Equation = ( y = ax²+bx+c , where c is the y intercept )
Vertex Quadratic Equation = ( y = a(x-h)² + k , where the vertex is (h,k) )
Factored Quadratic Equation = ( y = a ( x - R1 ) ( x - R2 ) , where R1 and R2 are roots )
Quadratic Formula = (-b±√(b²-4ac))/(2a)
Discriminant Formula = b² -4ac
Positive discriminant = 2 different real solutions
Negative discriminant = no real solutions
discriminant is 0 = repeated real number solution
Standard form of linear function = Ay + Bx = C
In systems of equations a single x or y value = one solution ( intersect at one point )
In systems of equations an untrue statement ( like 5 = 9 ) = zero solutions ( parallel lines )
In systems of equations two values that always equal each other ( like 3x = 6x - 3x ) = infinite solutions ( same line )
Square of a sum is ( a + b )² = ( a + b ) ( a + b ) = a² + 2ab + b²
Square of a different is ( a - b )² = ( a - b ) ( a - b ) = a² - 2ab + b²
Standard form slope = if Ax + By = C then -A/B is the slope
See Also11. Euler's Method - a numerical solution for Differential EquationsWhat Is The Center Of The Circle With The Equation (x-1)^2 + (y+3)^2= 9? A (1,3) B (-1,3) C (-1,-3) DThe Expression 3 X 7 - 4x8+2 Is Equivalent To Which Of The Following?A 3* (7 - 4) * (8 + 2)B (3 X 7)Determine F'(x) From The First Principle If , F(x) = -2x+bx+5Midpoint formula of ( x1, y1) and ( x2, y2 ) = ( (x1 + x2 ) / 2 ) , ( y2 + y2 ) / 2 )
Distance formula between (x1 , y1 ) and ( x2, y2 ) = sqrt ( ( x2 - x1 ) ² + ( y2 - y1 ) ² )
How to find the vertex of any parabola
when y = ax² + bx + c , h of ( h , k ) = (-b/2a)
Then substitute a into the main equation again to find the y value of the vertex ( k )
The midpoint of 2 zeroes ( in a quadratic ) is x-value of a vertex
Circle equation : ( x-h )² + ( y-k )² = r², where ( h, k ) is the center point
Central angles are proportional to the arc length they intersect
central angle degree / 360 degrees = arc length in radians / 2pi * r
Degrees to radians = degree * pi / 180
Radians to Degrees = 180 / pi * radians
for an arc on a circle with a central angle of theta
Length of arc = theta times r
central angle measure / total measure of an angle in circle = sector area / total circle area
For any sector in a circle with a central angle of theta
Area = ½ * theta * r²
(f o g)(x) = f(g(x))
(f * g ) ( x ) = f g(x) = f(x) g(x)
(f/g) ( x ) = f(x)/g(x)
mode = most common term in a set of terms
median = the middle number
mean = the average of the data set ( sum of terms divided by number of terms )
Sum of 2 cubes : a³ + b³ = ( a + b ) ( a² - ab + b² )
Difference of 2 cubes : a³ - b³ = ( a - b ) ( a² + ab + b² )
Speed = distance / time
Time = distance / speed
Parallel lines have the same slope
The magnitude ( how steep the line is ) of a slope is always positive = absolute value of slope
Perpendicular lines have opposite reciprocal slope
Sub in 0 for y to find the x intercept(s)
Sub in 0 for x to find the y intercept
Vertical asymptote = vertical line ( x = ? )
Horizontal asymptote = horizontal line ( y = ? )
If functions are symmetrical across y axis = even function
if f(-x) = f(x) then the function is an even function ( even degree )
if f(-x) = -f(x) then the function is an odd function ( odd degree )
To shift a graph up, ADD a constant outside the x
To shift a graph down, subtract a constant outside the x
To shift a graph to the left, ADD a constant inside the x
Frequency = number of times a value occurs in a data set
positive correlation = distribution of data points in a scatter plot show a positive slope
Normal distribution : Mean = median
Outlier = a data point that differs significantly from the other values in a set
Large outlier : mean > median
Small outlier : mean < median
outliers mainly impact the mean and have no effect on median
Standard deviation = measure of the amount of variability in a set of data. Measure of how far the individual data points are from the mean of the data
High standard deviation = spread out over a wide range of values
low standard deviation = data points are clustered around mean
Margin of Error = how far off the mean in a sample is compared to the true mean in a larger population ( like error bars )
The larger the standard the deviation the larger the margin of error
The larger the sample size the smaller the margin of error
Confidence interval = range of values within which true population mean is likely to fall with a given level of confidence ( ex: on average he gets 6 hours of sleep ± 1 hours. Confidence interval = 5-7 hours )
larger the standard deviation the larger the confidence interval
larger the sample size the smaller the confidence interval
To calculate the mean of combined data, add together the total sum of both sets of data and divide by the total number of values
Things to Remember ( Math ) Notes | Knowt (2024)
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