Pictures listed in order... from A-C
Answer:
q = -8, k = 2.
r = -6.
Step-by-step explanation:
f(x) = (x - p)^2 + q
This is the vertex form of a quadratic where the vertex is at the point (p, q).
Now the x intercepts are at -6 and 2 and the curve is symmetrical about the line x = p.
The value of p is the midpoint of -6 and 2 which is (-6+2) / 2 = -2.
So we have:
f(x) = 1/2(x - -2)^2 + q
f(x) = 1/2(x + 2)^2 + q
Now the graph passes through the point (2, 0) , where it intersects the x axis, therefore, substituting x = 2 and f(x) = 0:
0 = 1/2(2 + 2)^2 + q
0 = 1/2*16 + q
0 = 8 + q
q = -8.
Now convert this to standard form to find k:
f(x) = 1/2(x + 2)^2 - 8
f(x) = 1/2(x^2 + 4x + 4) - 8
f(x) = 1/2x^2 + 2x + 2 - 8
f(x) = 1/2x^2 + 2x - 6
So k = 2.
The r is the y coordinate when x = 0.
so r = 1/2(0+2)^2 - 8
= -6.
f(x) = sqrt [( x - 3) / (x - 5)]
well x cannot be 5 because that would make x - 5 = 0.
Also the fraction x - 3 / x - 5 cannot be negative because theres no real square root of a negative.
So x must be <= 3 or > 5
In interval notation the domain is ( -∞,3] or (5 , ∞)
Three A grows 1 meter in 110/45 = 2.44 years;
Three B grows 1 meter in 1840/110 = 16.72 years;
Because 2.44 < 16.73, the tree A grows faster than tree B.
