Answer:
(x²-10x+33)/(-8) = y
Step-by-step explanation:
The distance between any point on a parabola from both its focus and directrix are the same.
Let's say we have a point (x,y) on the parabola. We can then say that using the distance formula,
is the distance between (x,y) and the focus. Similarly, the distance between (x,y) and the directrix is |y-1| (I use absolute value here because distance is always positive). We can find this equation by taking the shortest distance from the point to the line. Because the closest point to the line will be the same x value as the point itself, the distance is simply the distance between the y value of the point and the y value of the directrix.
Equating the two equations given, we have
square both sides to get
(x-5)²+(y+3)²=(y-1)²
expand the y components
(x-5)² + y²+6y+9 = y²-2y+1
subtract y²+6y+9 from both sides
(x-5)² = -8y - 8
expand the x components
x²-10x+25 = -8y - 8
add 8 to both sides to isolate the -8y
x²-10x+33 = -8y
divide both sides by -8 to isolate y
(x²-10x+33)/(-8) = y
Answer:
Step-by-step explanation:
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The function f(x) = x2 - 8x + 7 rewritten by completing the square is x² - 8x + 16 = 9.
<h3>Rewrite the function by completing the square?</h3>
Given the function; f(x) = x² - 8x + 7
To rewrite by completing the square.
We simplify the function into a proper form to completing the square.
x² - 8x + 7 = 0
x² - 8x = -7
We create a trinomial square on the left side of the equation that is equal to the square of the half of b.
(b/2)² = (-4)²
Next, we add the term to both side of the equation.
x² - 8x + (-4)² = -7 + (-4)²
x² - 8x + 16 = 9
Therefore, the function f(x) = x2 - 8x + 7 rewritten by completing the square is x² - 8x + 16 = 9.
Learn more about completing the square method here: brainly.com/question/12356597
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Answer:
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Step-by-step explanation:
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