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Umnica [9.8K]
3 years ago
6

Write y=2x^2+8x+10 in vertex form?

Mathematics
2 answers:
muminat3 years ago
5 0
The answer is -2 you use the formula -b over 2a
soldi70 [24.7K]3 years ago
4 0
\bf y=2x^2+8x+10\impliedby \textit{let's start by grouping}
\\\\\\
y=(2x^2+8x)+10\implies y=2(x^2+4x+\boxed{?}^2)+10

hmmm we seem to be missing a value there, to get a "perfect square trinomial" from the group... what can that be?
hmm, well, recall, the middle term of a perfect trinomial, is 2 * [guy on the left] * [guy on the right]

now, the middle term, would be 4x, so, we know that 2 * x * [?] = 4x
well \bf 2\cdot x\cdot \boxed{?}=4x\implies \boxed{?}=\cfrac{4x}{2x}\implies \boxed{?}=2

so, that's our missing fellow, is 2, now, keep in mind, all we're doing is borrowing from our very good friend Mr Zero, 0, so, if we add 2², we have to also subtract 2²

thus   \bf y=2(x^2+4x+2^2-2^2)+10\\\\\\ y=2(x^2+4x+2^2)-2^2\cdot 2+10
\\\\\\
y=2(x+2)^2-8+10\implies y=2(x+2)^2+2

notice, the -2 was inside, with a common factor of 2, so it was really 2*-2², or -8 when it came out of the group

anyhow, that's the so-called "completing the square", and that's the vertex form of the parabola, whose vertex is clearly at -2, 2
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G(x)=(x^2+1)(3x-5) what is the value of g(4)?
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6 0
3 years ago
39/250 in simplest form
OleMash [197]
Getting the simplest form of a fraction is the same with getting its lowest term. Reducing fractions to its lowest term is a very simple thing to do. Here's how to simplify fractions:

There are two ways in simplifying fractions. The first method is to equally divide both numerator and denominator which results to only whole numbers. Getting the GCF (Greatest Common Factor) or GCD (Greatest Common Divisor) is the second method.

As to the fraction above, 39/250, the second method is applicable.
Let us get the GCF of 39 and 250
39= 1,3,13,39
250= 1, 2, 5,  10, 25, 50, 125, 250

Therefore, the GCF of 39 and 250 is 1. We can conclude then that 39/250 is already on its simplest form thus;
  <u>39</u>  ÷     <u>1</u> is equal to     <u>39</u>
 250       1                       250



7 0
2 years ago
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