Triangle A B C is shown. Angle B C A is a right angle. The length of hypotenuse A B is 5, the length of B C is 3, and the length
of A C is 4. What is the length of the side opposite Angle B? 3 units 4 units 5 units 6 units
1 answer:
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Answer: y = 2 (x minus one-half) squared minus StartFraction 27 Over 2 EndFraction
or
Step-by-step explanation:
Vertex form of equation : where (h, k) is the vertex of the parabola.
Hence, the vertex form of the equation is
Now, recall Descartes Rule of Signs. Check the picture below.
the +x part, gives us the positive Real zeros, and it depends on how many times the sign changes from term to term, notice in the picture, it changed 3 times, so the positive real ones are 3, or 3-2, namely 1, so 3 or 1.
the negative real ones, come from using -x as the argument on f(x), and as you can see in the picture, there was only 1 sign change, meaning the negative real zeros are only 1.
since, based on the fundamental theorem of algebra the polynomial has 4 roots at most then,
3 positive real ones, and 1 negative real one, no complex ones
or
1 positive real one, and 1 negative real one, and 2 complex ones
bear in mind that complex always come in pairs, never alone.
the +x part, gives us the positive Real zeros, and it depends on how many times the sign changes from term to term, notice in the picture, it changed 3 times, so the positive real ones are 3, or 3-2, namely 1, so 3 or 1.
the negative real ones, come from using -x as the argument on f(x), and as you can see in the picture, there was only 1 sign change, meaning the negative real zeros are only 1.
since, based on the fundamental theorem of algebra the polynomial has 4 roots at most then,
3 positive real ones, and 1 negative real one, no complex ones
or
1 positive real one, and 1 negative real one, and 2 complex ones
bear in mind that complex always come in pairs, never alone.