I think that the correct answer is f(-1)=-8 and f(0)=-5
I hope this helps :D
Find the line that is normal to the parabola at the given point
remember that normal means perpendicular
perpendicular lines have slopes that multiply to -1
we can use point slope form to write the equation of the line since we are given the point (1,0)
we just need the slope
take derivitive
y'=1-2x
at x=1
y'=1-2(1)
y'=1-2
y'=-1
the slope is -1
the perpendicular of that slope is what number we can multiply to get -1
-1 times what=-1?
what=1
duh
so
point (1,0) and slope 1
y-0=1(x-1)
y=x-1 is da equation
solve for where y=x-1 and y=x-x² intersect
set equatl to each other since equal y
x-1=x-x²
x²-1=0
factor difference of 2 perfect squares
(x-1)(x+1)=0
set to zero
x-1=0
x=1
we got this point already
x+1=0
x=-1
sub back
y=-1-(-1)²
y=-1-(1)
y=-1-1
y=-2
it intersects at (-1,-2)
The probability of rolling an even number on the first dice is 1/2(3/6)
The probability of rolling an even number on the first dice is also 1/2 (3/6)
So the probability of getting two even numbers on both dice is 1/2*1/2=1/4
Here's the info for f(x): We are going to find the slope of the line and then write the equation for the line using one of the given points. The coordinate points we are given are (0, 0) and (2, 4). Using the slope formula:
![m= \frac{y_{2} - y_{1} }{ x_{2}- x_{1} }](https://tex.z-dn.net/?f=%20m%3D%20%5Cfrac%7By_%7B2%7D%20-%20y_%7B1%7D%20%7D%7B%20x_%7B2%7D-%20x_%7B1%7D%20%20%7D%20)
gives us a slope equation of:
![m= \frac{4-0}{2-0}](https://tex.z-dn.net/?f=m%3D%20%5Cfrac%7B4-0%7D%7B2-0%7D%20)
and the slope is 2. Using the point (0, 0) to write the equation of the line for f(x) looks like this in the slope-intercept form of the equation:
![y- y_{1} =m(x- x_{1})](https://tex.z-dn.net/?f=y-%20y_%7B1%7D%20%3Dm%28x-%20x_%7B1%7D%29%20)
where m is the sloppe of 2 that we found and
![y_{1}](https://tex.z-dn.net/?f=%20y_%7B1%7D%20)
and
![x_{1}](https://tex.z-dn.net/?f=%20x_%7B1%7D%20)
are the coordinates of one of the points. It doesn't matter which one you choose; you will get the same answer whether you use (0, 0) or (2, 4): y-0=2(x-0) Distributing that 2 into the parenthesis and simplifying gives you the equation of y = 2x, or in our function notation, f(x) = 2x. Since f(x) is the first part of g(x), so far for g(x) we have that g(x) = 2x + k. Now we will do the same thing for g(x) that we did for f(x) as far as writing its equation down; we don't need to find the slope cuz the slope of g(x) is the function f(x). The equation for g(x), using the point (0, 2) (again, you could have used either point; I just picked (0, 2) cuz the other one has a decimal in it!): y - 2 = 2(x - 0). Distributing that 2 into the parenthesis gives you this: y - 2 = 2x - 0; y = 2x + 2. So 2 is your k value!
Answer:
-7x^3+8x^2+x-5
Step-by-step explanation:
We are simply adding the two functions:
f(x) + g(x) = (2x^2-5x^3+x-7) + (6x^2-2x^3+2) = 8x^2-7x^3+x-5 = -7x^3+8x^2+x-5