Answer:
Step-by-step explanation:
The parent function denotes the simplest function (free from any horizontal/vertical stretch/compression) that represents a family of functions. In this case the term 1/4 indicates a horizontal stretch and should be removed to find the parent function of . From here we're in simplest form, since
or others represent a completely different family of functions and cannot be obtained from horizontal/vertical stretches/compressions.
The centroid of a triangle divides the median of the triangle into 1 : 2
The measure of FQ is 18, while the measure of TQ is 6
Because point T is the centroid, then we have the following ratio
Where FT = 12.
Substitute 12 for FT in the above ratio
Express as fraction
Multiply both sides by 12
This gives
Divide 12 by 2
The measure of FQ is calculated using:
Substitute 12 for FT, and 6 for TQ
Add 12 and 6
Hence, the measure of FQ is 18, while the measure of TQ is 6
Read more about centroids at:
Answer:
f(r) = (x -1)(x -4+√7)(x -4-√7)
Step-by-step explanation:
The signs of the terms are + - + -. There are 3 changes in sign, so Descartes' rule of signs tells you there are 3 or 1 positive real roots.
The rational roots, if any, will be factors of 9, the constant term. The sum of coefficients is 1 -9 +17 -9 = 0, so you know that r=1 is one solution to f(r) = 0. That means (r -1) is a factor of the function.
Using polynomial long division, synthetic division (2nd attachment), or other means, you can find the remaining quadratic factor to be r^2 -8r +9. The roots of this can be found by various means, including completing the square:
r^2 -8r +9 = (r^2 -8r +16) +9 -16 = (r -4)^2 -7
This is zero when ...
(r -4)^2 = 7
r -4 = ±√7
r = 4±√7
Now, we know the zeros are {1, 4+√7, 4-√7), so we can write the linear factorization as ...
f(r) = (r -1)(r -4 -√7)(r -4 +√7)
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<em>Comment on the graph</em>
I like to find the roots of higher-degree polynomials using a graphing calculator. The red curve is the cubic. Its only rational root is r=1. By dividing the function by the known factor, we have a quadratic. The graphing calculator shows its vertex, so we know immediately what the vertex form of the quadratic factor is. The linear factors are easily found from that, as we show above. (This is the "other means" we used to find the quadratic roots.)
