12x^2-3y^2+24y-84=0
give the exact coordinates of any four points on the hyperbola

- toxicsugar22

12x^2-3y^2+24y-84=0
give the exact coordinates of any four points on the hyperbola

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- toxicsugar22

hi can u help me

- anonymous

more hyperbola's?

- toxicsugar22

yes

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## More answers

- anonymous

i'd love 2 help but don't know how to do them at all.

- myininaya

Just did as we did before find the x intercepts and the y-intercepts
to find x-intercepts let y=0
to find y-intercepts let x=0
both cases you were get a quadratic
use the quadratic equation
you can do it
i believe in you

- toxicsugar22

but im stuck i got 12x^2-3(0)^2+24(0)-84=0

- toxicsugar22

so i got 12x^2-0^2+0-84=0

- myininaya

so you have 12x^2-84=0 solve for x

- myininaya

add the 84 to both sides and then divide by 12 on both sides
then take the square root of both sides give you two x-intercepts

- toxicsugar22

so i got x^2=7

- toxicsugar22

so does x=7

- myininaya

and x=-7

- anonymous

To find the x-interceptGlossaryx-intercept The value of x at the point where a line or curve crosses the x-axis. , substitute in 0 for y and solve for x.
Expand the exponentGlossaryexponent A number that indicates the operation of repeated multiplication. (2) to the expressionGlossaryexpression A mathematical symbol, or combination of symbols, representing a value, or relation. Example: 2+2=4 .
Squaring a number is the same as multiplying the number by itself In this case, 0 squared is 0. Click here for more detail on this step
MultiplyGlossarymultiply To compute a product; to perform a multiplication. -3 by 0 to get 0.
Remove the parenthesesGlossaryparentheses Marks of inclusion (symbols: ( and ) ). Parentheses is the plural form of parenthesis. around the expressionGlossaryexpression A mathematical symbol, or combination of symbols, representing a value, or relation. Example: 2+2=4 0.
MultiplyGlossarymultiply To compute a product; to perform a multiplication. 24 by each termGlossaryterm Any expression written as a product or quotient. Example: 2xy , , or inside the parenthesesGlossaryparentheses Marks of inclusion (symbols: ( and ) ). Parentheses is the plural form of parenthesis. . Click here for more detail on this step
CombineGlossarycombine To join, or bring together. all similarGlossarysimilar Two polygons are similar if their corresponding sides are proportional. expressionsGlossaryexpression A mathematical symbol, or combination of symbols, representing a value, or relation. Example: 2+2=4 . Click here for more detail on this step
Since -84 does not contain the variableGlossaryvariable A letter used to represent a number value in an expression or an equation. to solve for, move it to the right-hand side of the equationGlossaryequation A mathematical statement that says two expressions have the same value; any number sentence with an = . by adding 84 to both sides.
DivideGlossarydivide To perform the operation of division. each termGlossaryterm Any expression written as a product or quotient. Example: 2xy , , or in the equationGlossaryequation A mathematical statement that says two expressions have the same value; any number sentence with an = . by 12.
Simplify the left-hand side of the equationGlossaryequation A mathematical statement that says two expressions have the same value; any number sentence with an = . by canceling the common factorsGlossaryfactor One of two or more expressions that are multiplied together to get a product. . Click here for more detail on this step
Simplify the right-hand side of the equationGlossaryequation A mathematical statement that says two expressions have the same value; any number sentence with an = . by simplifying each termGlossaryterm Any expression written as a product or quotient. Example: 2xy , , or . Click here for more detail on this step
Take the squareGlossarysquare A quadrilateral with four equal sides and four angles. rootGlossaryroot The root of an equation is the same as the solution to the equation. of both sides of the equationGlossaryequation A mathematical statement that says two expressions have the same value; any number sentence with an = . to eliminateGlossaryeliminate To remove, to get rid of. the exponentGlossaryexponent A number that indicates the operation of repeated multiplication. on the left-hand side.
First, substitute in the + portion of the to find the first solutionGlossarysolution The value of a variable that makes an equation true. .
Next, substitute in the - portion of the to find the secondGlossarysecond A unit of measure for angles equal to 1/60 of a minute. solutionGlossarysolution The value of a variable that makes an equation true. .
The complete solutionGlossarysolution The value of a variable that makes an equation true. is the result of both the + and - portions of the solutionGlossarysolution The value of a variable that makes an equation true. .
To find the y-interceptGlossaryy-intercept The value of y at the point where a curve crosses the y-axis. , substitute in 0 for x and solve for y.
Expand the exponentGlossaryexponent A number that indicates the operation of repeated multiplication. (2) to the expressionGlossaryexpression A mathematical symbol, or combination of symbols, representing a value, or relation. Example: 2+2=4 .
Squaring a number is the same as multiplying the number by itself In this case, 0 squared is 0. Click here for more detail on this step
MultiplyGlossarymultiply To compute a product; to perform a multiplication. 12 by 0 to get 0.
Remove the parenthesesGlossaryparentheses Marks of inclusion (symbols: ( and ) ). Parentheses is the plural form of parenthesis. around the expressionGlossaryexpression A mathematical symbol, or combination of symbols, representing a value, or relation. Example: 2+2=4 0.
CombineGlossarycombine To join, or bring together. all similarGlossarysimilar Two polygons are similar if their corresponding sides are proportional. expressionsGlossaryexpression A mathematical symbol, or combination of symbols, representing a value, or relation. Example: 2+2=4 .
MultiplyGlossarymultiply To compute a product; to perform a multiplication. each termGlossaryterm Any expression written as a product or quotient. Example: 2xy , , or in the equationGlossaryequation A mathematical statement that says two expressions have the same value; any number sentence with an = . by -1. Click here for more detail on this step
FactorGlossaryfactor One of two or more expressions that are multiplied together to get a product. out the GCFGlossaryGCF G reatest C ommon F actor; the largest number that divides two or more numbers evenly. of 3 from each termGlossaryterm Any expression written as a product or quotient. Example: 2xy , , or in the polynomialGlossarypolynomial An algebraic expression consisting of one or more summed terms, each term consisting of a constant multiplier and one or more variables raised to integral powers. . Click here for more detail on this step
FactorGlossaryfactor One of two or more expressions that are multiplied together to get a product. out the GCFGlossaryGCF G reatest C ommon F actor; the largest number that divides two or more numbers evenly. of 3 from
DivideGlossarydivide To perform the operation of division. both sides of the equationGlossaryequation A mathematical statement that says two expressions have the same value; any number sentence with an = . by 3. Dividing 0 by any non-zero number is 0.
SetGlossaryset A well-defined group of objects. each of the factorsGlossaryfactor One of two or more expressions that are multiplied together to get a product. of the left-hand side of the equationGlossaryequation A mathematical statement that says two expressions have the same value; any number sentence with an = . equal to 0.
Use the quadratic formulaGlossaryformula An equation that states a rule or a fact. to find the solutionsGlossarysolution The value of a variable that makes an equation true. . In this case, the values are a=1, b=-8, and c=28.
where
Use the standard form of the equationGlossaryequation A mathematical statement that says two expressions have the same value; any number sentence with an = . to find a, b, and c for this quadratic.
a=1, b=-8, and c=28
Substitute in the values of a=1, b=-8, and c=28.
MultiplyGlossarymultiply To compute a product; to perform a multiplication. -1 by each termGlossaryterm Any expression written as a product or quotient. Example: 2xy , , or inside the parenthesesGlossaryparentheses Marks of inclusion (symbols: ( and ) ). Parentheses is the plural form of parenthesis. . Click here for more detail on this step
Simplify the section inside the radicalGlossaryradical A root sign (symbol: ). . Click here for more detail on this step
Simplify the denominatorGlossarydenominator The bottom part of a fraction. of the quadratic formulaGlossaryformula An equation that states a rule or a fact. . Click here for more detail on this step
First, solve the + portion of
Simplify the expressionGlossaryexpression A mathematical symbol, or combination of symbols, representing a value, or relation. Example: 2+2=4 to solve for the + portion of the Click here for more detail on this step
Next, solve the - portion of
Simplify the expressionGlossaryexpression A mathematical symbol, or combination of symbols, representing a value, or relation. Example: 2+2=4 to solve for the - portion of the Click here for more detail on this step
The final answer is the combinationGlossarycombination A selection in which order has no importance. of both solutionsGlossarysolution The value of a variable that makes an equation true. .
These are the x and y interceptsGlossaryintercept The x-intercept of a line or curve is the point where it crosses the x-axis, and the y-intercept of a line or curve is the point where it crosses the y-axis. of the equationGlossaryequation A mathematical statement that says two expressions have the same value; any number sentence with an = .
No y-interceptGlossaryy-intercept The value of y at the point where a curve crosses the y-axis.

- anonymous

sorry if this is too long. but i hope it helps...

- myininaya

so toxic now we want to find y-intercetps so let x=0
what do you get?

- anonymous

##### 1 Attachment

- anonymous

go to mathway.com
it explains thoroughly how to do this problem if u enter it. good luck

- toxicsugar22

12(0)^2-3y^2+24y-84=0

- toxicsugar22

0^2-3y^2+24y-84=0

- myininaya

oh yeah toxic did take square root of boths on that pervius equation?

- toxicsugar22

so x^2=7

- myininaya

x=sqrt{7}
x=-sqrt{7} is what you got right?

- toxicsugar22

so okay it is (0,-sqrt{7})

- myininaya

and (0,sqrt{7})
but there are only two points
we need to find the other two

- myininaya

so what does that equation you just wrote with zeros look without zeros

- toxicsugar22

can i do this tommorow i cant think it midnight where i am

- toxicsugar22

ill be on tommorrow

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