Which graph best represents y = −x2 + 6x − 1?
2 answers:
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Answer:
- 8.5 feet
Explanation:
The function that can determine the distance from a point on the bottom edge of the banner to the floor is:
That function is a quadratic function which means that it is a parabola. Given that the coefficient of the quadratic term (0.25) is positive, the parabola open upwards, and the vertex is the lowest point of the parabola and it represents how high above the floor is the lowest point on the bottom edge of the banner.
So, you need to find the vertex of the parabola.
I will complete squares to find the form A(x -h)² + k, where h and k are the coordinates of the vertex (h, k).
Hence, the vertex (h,k) is (2, 8.5), meaning that the lowest point on the bottom edge of the banner is at 2 feet from the left edge of the banner and 8.5 feet above the floor.
Answer:
a) , b)
,
, c)
, d)
Step-by-step explanation:
a) Let derive the function:
is undefined when denominator equates to zero. The critical point is:
b) when numerator equates to zero. That is:
This equation shows two critical points:
,
c) The critical points found in point b) and the existence of a discontinuity in point a) lead to the conclusion of the existence local minima and maxima. By plotting the function, it is evident that corresponds to a local maximum. (See Attachment)
d) By plotting the function, it is evident that corresponds to a local minimum. (See Attachment)
