C. multiply the second equation by two. Then add the equations
Answer:
A) f(x) = |x|
B) f(x) = -|x+3| + 3
Step-by-step explanation:
Absolute value functions
The general form of an absolute value function is f(x) = a|x-b| +c
a indicates the 'amplitude' or multiplier
b indicates horizontal shift
c indicates vertical shift
The turning point of f(x) = |x| is (0, 0)
a = y/x when b = 0 and c = 0
A) f(x) = |x|
Since the turning point is still (0, 0) there is no horizontal nor vertical shift, meaning b = 0 and c = 0
We have the point (2, 2), thus a = 2/2 = 1
f(x) = a|x-b| + c
f(x) = |x|
B) f(x) = -|x+3| + 3
The turning point is at (-3, 3) b = -3 and c = +3
We have the point (3, -3), thus a = y/x = -3/3 = -1
f(x) = a|x-b| + c
f(x) = (-1) (|x-(-3)|) + (+3)
f(x) = -|x+3| + 3
For given problem:
Put midpoint of ellipse, (0,0) at epicenter of bridge at
ground level.
Specified length of vertical major axis = 70=2a
a=35
a^2=1225
Equation of ellipse:
x^2/b^2+y^2=1
plug in coordinates of given point on ellipse(25, 10)
25^2/b^2 + 10^2/a^2 = 1
625/b^2 + 100/1225=1
625/b^2 = 1 - 100/ 1225 = .918
b^2 = 625/.918 ≈ 681
b ≈ 26.09
length of minor axis = 2b = 2(26.09) ≈ 52.16 ft
Span of bridge ≈ 52.16 ft
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