How do you find the focus, directrix and sketch $y = x^{2} - 2 x$ $y=x^2-2x$ ?

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How do you find the focus, directrix and sketch $y = x^{2} - 2 x$ $y=x^2-2x$ ?

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Answer 1 · 2017-01-19T17:05:55

When given, $y (x) = a x^{2} + b x + c$ $y(x) = ax^2 + bx + c$
$f = \frac{1}{4 a}$ $f = 1/(4a)$
$h = - \frac{b}{2 a}$ $h = -b/(2a)$
$k = y (h)$ $k = y(h)$
The focus is the point $(h, k + f)$ $(h, k + f)$
The equation of the directrix is $y = k - f$ $y = k - f$

Explanation:

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

$a = 1, b = - 2, and c = 0$ $a = 1, b = -2, and c = 0$

$f = \frac{1}{4 (1)}$ $f = 1/(4(1))$

$f = \frac{1}{4}$ $f = 1/4$

$h = - \frac{- 2}{2 (1)}$ $h = - (-2)/(2(1))$

$h = 1$ $h = 1$

$k = y (1)$ $k = y(1)$

$k = 1^{2} - 2 (1)$ $k = 1^2 - 2(1)$

$k = - 1$ $k = -1$

The focus is the point, $(1, - 1 + \frac{1}{4}) = (1, - \frac{3}{4})$ $(1, -1 + 1/4) = (1, -3/4)$

The equation of the directrix is:

$y = - 1 - \frac{1}{4}$ $y = -1 - 1/4$

$y = - \frac{5}{4}$ $y = -5/4$

Here is a graph of the parabola, the focus and the directrix.

![Desmos.com]( useruploads.socratic.org )

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How do you find the focus, directrix and sketch $y = x^{2} - 2 x$ $y=x^2-2x$ ?

1 Answer

Explanation:

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