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25 Cards in this Set
- Front
- Back
Commutative Property
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ab = ba
a+b = b+a |
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Associative Property
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3+(5+2) = 5+(3+2)
3(5*2)= 5(3*2) |
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Distributive
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3(5+2) = (3*5)+(3*2)
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When solving inequalities...
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solve like a regular equation.
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When solving absolute value inequalities...
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ex. /2x-1/<15
turns into 15</2x-1/<15 |
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A relation is a function
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all of the x's are unique
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When solving absolute value inequalities with an "or-equal-to" sign...
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The answer will be:
Either a or b. |
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to find slope...
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the change in y over the change in x
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Formula for direct variation
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y=kx
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When graphing peicewise functions...
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graph the top equations as one line and the bottom equations as another line.
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when graphing absolute value functions...
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vertex = (h,k)
when /x-h/+k |
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when solving Linear Systems...
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substitute or complete the square
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To tell how many solutions there are...
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same line= infinite solutions
undetermined= no solution determined solution= one solution |
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When graphing linear inequalities
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shade in the different lines. Where the darkest shading is, is the solution area.
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When finding max and min...
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graph all of the constraints until you have the darkest shaded region. Plug the vertices of that region (crooked line) into the orinal equation.
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When finding matrices Determinants...
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cross multiply the matrix and add the two products together
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When multiplying two matrices together...
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top row * first column, first row * second column, etc.
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Performing operations with matrices
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follow PEMDAS, and multiply a regular number by every number in the matrix when necessary
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Cramer's Rule
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when you have ax+by=c and dx+cy=f, put it into the matrix a-b-d-e (left to right, top to bottom)
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To find an inverse
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switch the top left and bottom right, and negate the top right and bottom left.
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When completing the square...
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put it in ax(squared)+bx=-c form. Add 25 to both sides of the equation. Factor the side without the "C". Find the square rool of both sides of the equation. Solve.
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When solving with the quadratic formula.
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substitute the standard equation into the quadratic formula and solve.
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Finding the discriminant of a standard equation
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Use Cramer's Rule and then find the determinant.
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When solving an absolute value inequality...
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ex /2x-5/<9
becomes 9</2x-5/<9 |
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When solving for an absolute value equation...
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Solve for case #1 (positive answer in the origional equation) and case #2 (negative answer in the origional equation)
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