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34 Cards in this Set
- Front
- Back
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Write the standard form of the equation of a circle with endpoints. |
(X1+X2)/2 , (Y1-Y2)/2 (x-h)^2 + (y-k)^2 = r^2 Solve, don't worry about r^2 that's just the answer for it without square rooting. Put back into second equation with new points. |
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Write the slope intercept form of a line that goes through a point and is parallel to another line. |
Put the line equation into y=mx+b format. Put the point into the question to find B. Slopes are the same. |
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Write the slope intercept form of a line that goes through a point and is perpendicular to another line. |
Put the equation into y=mx+b format. The slope is the reciprocal. Flip the fraction and sign. Plug in and solve for B. |
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You have two solutions that need to mix in order to form another solution with a certain amount. |
x=ml first solution y=ml second solution Put x+y=the final amount into y= form Multiply percent by amount, percent by amount, then equal to final percent and amount. Solve for x. |
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Twice as long as wide. Given final area. |
x= width y= length Y=2x xy=total amount Insert and solve |
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Solve by factoring |
Multiply a and c Find a number that multiplies to the new number, but adds up to b. Insert those into the equation instead of b. Factor out commons. You have your two parenthesis. Set them to equal zero and solve. |
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Solve by completing the square. |
Add constants into right side Factor out from the two on the left, coefficient has to be 1 Divide the outstanding number Insert (b/2)^2 on both sides. Find the factors of your new left equation. They should be able to rise to the second power. Square root that and the other side. Add or subtract your constant on the left Simplify the fraction under the radical if needed. The top number may be a perfect square. Cannot have a radical on the bottom. Multiply both top and bottom by radical. Your answer should include plus or minus. |
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Solve by using the quadratic formula |
x=-b+/-(square root)b^2-4(a)(c) ALL OVER 2a Don't forget to simplify |
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Solving various types of equations: with a radical |
First move anything that isn't connected to the radical to the other side. Divide by anything outside the radical. Square the radical and the other side. Do anything you need to do moving wise once you square the opposing side. Arrange to equal zero and solve for two parenthesis. Set those equal to zero and solve. Plug back into the equation to look for extraneous solutions. |
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Solving a two symbol inequality |
Take out everything from the center and apply it to the outside numbers. |
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Solve an absolute value equation |
Remove all constant to the opposite side Solve the equation with a positive end and a negative end. |
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Solving an absolute value that's a fraction and it's an inequality |
Mostly the same. Solve once with positive and once with negative. Then place them into an inequality. |
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Evaluating functions with two equations, given f(x) equals a single number |
Implement it into the correct of the available equations and solve. |
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Difference quotient |
(x+h) - (x) / h |
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Determine domain and range on a graph |
Identify domain by x axis and range by y axis. For domain, the dots will tell you whether it's equal too or not. For range, assume it's equal to. |
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Increase and decrease on a graph |
Defined by the x axis. Anything not directly on a dot is equal to. |
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Defining maximums and minimums |
At (y value) when x=(value) |
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Graph a piece wise function |
Graph like normal through the calculator. Define by the second half given. |
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Linear, quadratic, cubic, reciprocal, greatest integer and square root functions. |
x, x^2, x^3, 1/x, [x], (square root)x |
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Reflect over y/x axis |
The negative is in the parent function/the negative is outside the parent function |
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Vertical shrink/stretch and horizontal shrink/stretch |
Vertical shrink: outside the parent function, fraction. Stretch: whole number. Horizontal shrink: whole number by the parent function. Stretch: fraction by the parent function |
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+/- in the parent function +/- outside the parent function |
-= right +=left -=down +=up |
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Determine if a function is odd, even, or neither. |
Odd= every part of the equation changes. Cannot be if an equation has a constant. Also can happen in a fraction question, if either of them are odd the answer is odd (-1/1=-1) Even= if everything stays the same in an equation. Neither= if there is a mixed result. |
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Find (fog) and it's domain |
place the "g" equation into the "f" equation, solve to get another equation by putting it equal to 0. Take the original "g" equation and have it greater than or equal to 0. Solve, then solve again with x being negative. |
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Find the inverse function and it's domain and range. |
swap the x and y. solve for y. If it's a fraction, multiply the bottom onto the other side. Distribute. Put all the numbers with x or y on one side, and everything else on the other. Factor out the y. Divide what's left onto the other side. |
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Find the 0's of a function algebraically. (4 numbers) |
Separate them into two different parenthesis that are adding to each other. Factor out and you have your final two parenthesis. Put those equal to 0 and solve. If one has been square rooted, it's plus or minus. |
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add/subtract something in the form a + bi |
Adding- add like terms. Subtracting- change the signs of the numbers in the parenthesis, combined like terms. |
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Multiply something into the form a + bi |
FOIL. Combined like terms. |
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Divide something into form a+bi |
Multiply the bottom to the bottom and top. Switch the sign that's between the two numbers. FOIL for both. Put them on their respective parts of the fraction. SIMPLIFY. |
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Evaluate the power. i^x |
divide the number by 4. Evaluate the answer by whatever number is left. 2= -1 3= -i 4= 1 |
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Multiply something into the form a+bi with radical expressions. |
SIMPLIFY. Anything with a negative needs an i on the outside to make it positive (if it's a radical). Simplify it down to two numbers if necessary. FOIL and combined like terms. |
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Find a solution for equations with three numbers in the form a+bi
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Insert into the quadratic formula and solve. |
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solve an equation with fractions as it's exponents |
Place the x's into their own parenthesis to the power of 1/(a) or whatever number was the denominator of the first fraction. Have that parenthesis be to the power of the numerator of the first fraction. Have w equal the exponent that's in the parenthesis, so that w to whatever number was the denominator for x will equal a full x. Place these into the equation and solve to get two more parenthesis. If the first exponent is say 4 for example, the w inside the parenthesis will be to the 2nd power. place each of these individually to 0 and solve. Answer will likely be plus or minus if square rooted. There's one more step. Ask teacher. |
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Solve a simple equation such as 2x^2 + x > 1 |
Move all three numbers to one side and favor to make four numbers, so that you'll end up with the two parenthesis. The inequality will either face one way or the other for both (They will match) state this. You will select two to see which is right. Ask teacher. |
