Graph of the equation $y = 2 x - x^{2}$ is

Parabola

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Ellipse

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Hyperbola

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Circle

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Solution

The correct option is D Parabola
$y = 2 x - x^{2}$

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

$y = - (x^{2} - 2 x + 1 - 1)$

$y = - {(x - 1)^{2} - 1}$

$y = - (x - 1)^{2} + 1$

$y - 1 = - (x - 1)^{2}$

$(y - 1) = - 4 \times \frac{1}{4} (x - 1)^{2}$

The equation is of the form $Y^{2} = 4 a X$ where $Y = y - 1$ and $X = x - 1$

So, the graph is a parabola with vertex at $(1, 1)$

Suggest Corrections

Similar questions

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