Let's complete the square
f(x) = x^2 + 6x + 8
y = x^2 + 6x + 8
y-8 = x^2 + 6x
y-8+9 = x^2+6x+9 .... see note below
y+1 = (x+3)^2
y = (x+3)^2-1
note: I added 9 to both sides due to taking half of the 6, and then squaring that result.
We'll restrict x such that 
to ensure that this function is one-to-one.
Now we need to swap x and y, and solve for y to get the inverse
y = (x+3)^2 - 1
x = (y+3)^2 - 1
x+1 = (y+3)^2
(y+3)^2 = x+1
y+3 = sqrt(x+1)
y = sqrt(x+1)-3
g(x) = sqrt(x+1)-3 is the inverse
The graph is shown below. The original function is in red. The inverse is in blue. The inverse is the result of reflecting the red curve over the dashed line y = x. So this explains why x and y swap places. Consequently, the domain and range also swap as well.
The monomial x would be the length of the sports banner.
-We know this because we typically use a basic variable for the thing that does not change. In this case, the length of the sports banner remains the same.
The second degree term in the expression would be the increase in area of the culture banner to make the sports banner.
-We can tell this because when we increase the width of the banner by 12, the resulting polynomial is 12x larger than x^2 (which was the original area of the culture banner.
The binomial expression x + 12 would be the width of the sports banner.
-Since we are increasing the width of the culture banner from x, x + 12 would represent the new width of the sports banner.
The first degree term in the expression would be the area of the culture banner.
-Because side of the culture banner is the same before the increase, multiplying x by itself will give you an area of x^2. This is the first degree term.
Answer:
c
Step-by-step explanation:
x²+y²+4x+6y=0
compare with x²+y²+2gx+2fy+c=0
centre is (-g,-f)=(-2,-3)
radius=√(g²+f²-c)=√((-2)²+(-3)²-0)=√13
Answer:
(9,2)
Step-by-step explanation:
To find the x coordinate of the midpoint, average the x coordinates of the endpoints
(14+4)/2 = 18/2 = 9
To find the y coordinate of the midpoint, average the y coordinates of the endpoints
(-8+12)/2 = 4/2 = 2
Answer:
Step-by-step explanation:
