How to use two terms to find a1,d, and an For the arithmetic sequence?
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Answer:
Zeros : 1 , -1, 3
Degree : 4
End Behaviour : At x-> ∞ f(x) -> ∞ and x->-∞ f(x) -> ∞
Y - intercept : -3
Extra Points: (0,-3), (2,-3)
Step-by-step explanation:
f(x) = 0 to find the zeros
Clearly x = -1,1,3
Here 1 is a repeating root as it is (x-1)²
Degree is highest power of x in f(x)
Clearly it is x*x²*x = x⁴ is the maximum power of x
Thus degree is 4
Looking at end behavior we substitute x->∞ and x-> -∞
Clearly f(x)>0 as all terms are positive and f(x)->∞
Similarly when x->-∞
f(x)>0 as 2 terms are -ve and their product is positive thus f(x)-> ∞
Y-Intercept is f(0)
f(0) = (0+1)(0-1)²(0-3) = 1*1*-3 = -3
Thus Y-Intercept is -3
Substitute x = 0 , 2 for extra points
Thus f(0) = -3
and f(2) = -3
Thus points on the graph (0,-3), (0,2)
We can use all this information to draw a graph remember that 1 is a repeating root so that will be a point of minima. The graph is a parabola that passes through x-axis at x = -1, 3.
Check the picture below.
since the distance AB cannot be a negative value, thus is not -3-√(130).
since the distance AB cannot be a negative value, thus is not -3-√(130).
1. Take an arbitrary point that lies on the first line y=3x+10. Let x=0, then y=10 and point has coordinates (0,10).
2. Use formula to find the distance from point
to the line Ax+By+C=0.
The second line has equation y=3x-20, that is 3x-y-20=0. By the previous formula the distance from the point (0,10) to the line 3x-y-20=0 is:
.
3. Since lines y=3x+10 and y=3x-20 are parallel, then the distance between these lines are the same as the distance from an arbitrary point from the first line to the second line.
Answer: .