Answer:
Step-by-step explanation:
Hello,
degree 5
4 is a zero of multiplicity 3 -> (x-4)^3 is a factor
-4 is the only other zero, so the multiplicity is 5-3=2 -> (x+4)^2 is a factor
leading coefficient is 4 so we can write
If there is something that you do not understand or you are blocked somewhere let us know what / where.
Thank you.
Answer:
Step-by-step explanation:
The common denominator of both fractions is 8. Therefore,, divide the denominator of each fraction, then multiply what you get by the numerator of each fraction.
Thus:
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