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- Learn more:✕This summary was generated using AI based on multiple online sources. To view the original source information, use the "Learn more" links.For Two Numbers: The formula for addition of squares of any two numbers x and y is represented by; x2 + y2 = (x + y)2– 2ab ; x and y are real numbers Proof: From the algebraic identities, we know; (x + y) 2 = x 2 + y 2 + 2ab Therefore, we can write the above equation as; x 2 +y 2 = (x + y) 2 – 2abbyjus.com/maths/sum-of-squares/The formulas for the squares of the sum and the difference are: (x+y)2 = x2 +2xy+ y2 (x−y)2 = x2 −2xy+ y2 (x + y) 2 = x 2 + 2 x y + y 2 (x − y) 2 = x 2 − 2 x y + y 2www.cuemath.com/algebra/x-squared/
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How do you factor x^2 - y^2 ? + Example - Socratic
Jul 7, 2015 · In general, if you spot something in the form a2 −b2 then it can be factored as (a −b)(a + b) For example: 9x2 − 16y2 = (3x)2 − (4y)2 = (3x −4y)(3x + 4y) Answer link. This is known as a difference of squares.
Completing the Square - Algebra - Socratic
So long as we are happy calculating square roots, we can now solve any quadratic equation. Completing the square is also useful for getting the equation of a circle, ellipse or other conic …
If y varies directly as the square of x. When x = 2, y = 20
Apr 5, 2017 · Explanation: Note - the square of x is expressed as x2. ⇒ y ∝ x2. Make into an equation by introducing k, the constant of variation. ⇒ y = k × x2 = kx2. To find k, use the …
How do you find the center and radius for #x^2 + y^2 - 6x - 4y
Nov 1, 2016 · XXXx2 + y2 − 6x − 4y −12 = 0. into the standard form for the equation of a circle. Group the x and y terms separately and "move" the constant to the right side of the equation: …
How do you solve by completing the square: - Socratic
Apr 1, 2015 · How do you complete the square when a quadratic equation has a coefficient? Why is completing the square useful? How do you find the missing value to create a perfect square …
Completing the Square - Precalculus - Socratic
Completing the square is a method used to solve a quadratic equation, #ax^2+bx+c#, where #a# must be #1#. The goal is to force a perfect square trinomial on one side and then solving for …
How do you simplify #sqrt(x^2+y^2)#? - Socratic
Jan 25, 2018 · There's no way to factor #x^2+y^2# to get a perfect square. The only real way to simplify this expression is by using math that's at a higher than algebra level, so for all intents …
How do you solve an equation by completing the square?
Mar 9, 2015 · An expression like #x^2+6x# may be thought of as an "incomplete" square. To make it complete, we'd need to add #n^2# to the expression. We can figure out what to use for #n# …
Does the equation x^2+y^2=1 describe a function? | Socratic
May 26, 2017 · Subtract x^2 from both sides to get: y^2 = 1-x^2 Take the square root of both sides, allowing for both square roots, to get: y = +-sqrt(1-x^2) We see that this does not define …
The square of x is equal to 4 times the square of y. If x is 1 more ...
Feb 9, 2016 · You can make a quick check if #x# and #y# were computed correctly: the square of #x# is #(1/2)^2 = 1/4# , the square of #y# is #(-1/4)^2 = 1/16# . The square of #x# is indeed …
The Quadratic Formula - Precalculus | Socratic
The quadratic formula is represented as: #(-B +- sqrt(B^2-4AC))/(2A) = x#... where x represents the x-coordinate of the zero. If #B^2 -4AC <0#, we will be dealing with complex roots, and if …
Is the equation x^2+y^2=4 a function? - Socratic
Mar 25, 2017 · And the answer is no - for essentially all the x values (excepting x=pm2), there are two y values for each x value. This is often called the "vertical line test" - if you draw a vertical …
If y is directly proportional to the square of x, when x=4 y = 25, …
Jul 18, 2015 · Find the quadratic expression. y would be in the form: y = ax^2 25 = a (4)^2 --> 25 = 16a --> a = 25/16 The expression would be: y = (25x^2)/16 Check: x = 4 --> y = 25.
Vertex Form of a Quadratic Equation - Algebra | Socratic
How do you find the vertex, x-intercept, y-intercept, and graph the equation #y=-4x^2+20x-24#? How do you write #y=9x^2+3x-10# in vertex form? What is the vertex of #y=-1/2(x-4)^2-7#?
Y varies inversely as the square of x when x=6 y=4, how do
May 29, 2017 · Explanation: y varies inversely as the square of x means: y = k x2. Solving for k: k = x2y. k = (6)2(4) k =. To find y when x = 2, we go back to the orinal equation: y = k (2)2.
How do you convert x^2 + y^2 = 16 into polar form? - Socratic
Nov 21, 2015 · By definition, you pass from (x,y) coordinates to (rho, theta) coordinates by: rho = sqrt (x^2+y^2) theta = arctan (y/x) ( with some changes depending on the sign of x and y). So, …
Is x^2+y^2=9 a function? + Example - Socratic
Aug 1, 2015 · #x^2+y^2 = 9# is not a function Explanation: In order for an equation to represent a function any single value of #x# must have at most one corresponding value of #y# which …
How do you graph x^2+y^2=4? - Socratic
Feb 28, 2016 · y2 = 4 −x2. Take the square root of both sides. y = √4 − x2. Now write it as. y = ± √4 −x2. '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~. Calculate and plot a series of points using …
How do you convert x^2+y^2=x to polar form? - Socratic
May 8, 2016 · Explanation: To convert to polar form, substitute: {x = rcosθ y = rsinθ. then simplify: So: x2 +y2 = x. becomes: (rcosθ)2 + (rsinθ)2 = rcosθ. The left hand side simplifies as follows:
How do you decide whether the relation # x^2 + y = 81 ... - Socratic
May 29, 2018 · Subtracting y from both sides of the equation, we get x^2 = -y+81 which is not a function: for every value y we may choose, assuming -y+81 is positive, we have ambiguity on …
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