The "standard" parabola with roots 0 and 2 is
All multiples of this parabola, i.e.
have the same roots. We can choose the factor such that the parabola passes through the desided point: if we plug 1, 5 for x, y we have
So, our claim is that the parabola
has roots 0 and 2 and vertex at (1, 5).
You can easily verify this: the roots are guaranteed by the fact that we can write the equation as
The vertex must be at x=1, because it's the midpoint of the roots. Moreover, if we evaluate the function at x=1 we have
as required.
Answer:
(1)-5x (2)-3x and 0x
Step-by-step explanation:
(1) -7x-2y=5
-7x-12=5
(2) y=-8x+5=-3x
y=-5x+5=0x
The division algorithm is (y+6)(y-2) +(-2).
<h3>What is Division Algorithm ?</h3>
When A and B are two expressions or numbers and Q and R are quotient and remainder respectively where r is always less than the divisor
The answer can be written in the form of
Q*D +R
The given expression is
on dividing
Quotient Q = y+6
Remainder = -2
So it can be written as
(y+6)(y-2) +(-2)
To know more about Division Algorithm
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Answer:
The width is:
The length is
Step-by-step explanation:
The given rectangle has area given algebraically by the function:
The width of the rectangle is the greatest common factor of , and
That is the width is:
We now divide the area by the width to obtain the length of the rectangle:
This simplifies to: