How do you identity if the equation $y + 4 = {(x - 2)}^{2}$ $y+4=(x-2)^2$ is a parabola, circle, ellipse, or hyperbola and how do you graph it?

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How do you identity if the equation $y + 4 = {(x - 2)}^{2}$ $y+4=(x-2)^2$ is a parabola, circle, ellipse, or hyperbola and how do you graph it?

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Answer 1 · 2017-02-07T07:09:31

The given equation is a Parabola

Explanation:

Given -

$(y + 4) = {(x - 2)}^{2}$ $(y+4)=(x-2)^2$

Let us rewrite the equation in a know form

$y + 4 = x^{2} - 4 x + 4$ $y+4=x^2-4x+4$
$ycancel (+4)-x^2-4xcancel(-4)=0$

$-x^2-4x+y=0$

Let us have the coics section equation

$Ax^2+Cy^2+Dx+Ey+F=0$

If the product of the coefficient of $x^2$ and $y^2$ is equal to zero, then the given equation is a Parabola.

In the given equation there is no $y^2$ term. The coefficient of $y^2$ is zero. Hence the product of the coefficients of $x^2$ and $y^2$ is equal to zero.

The given equation is a Parabola.

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How do you identity if the equation $y + 4 = {(x - 2)}^{2}$ $y+4=(x-2)^2$ is a parabola, circle, ellipse, or hyperbola and how do you graph it?

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Explanation:

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How do you identity if the equation y+4=(x-2)^2y+4=(x−2)2y+4=(x-2)^2 is a parabola, circle, ellipse, or hyperbola and how do you graph it?

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How do you identity if the equation $y + 4 = {(x - 2)}^{2}$ $y+4=(x-2)^2$ is a parabola, circle, ellipse, or hyperbola and how do you graph it?