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Ulleksa [173]
3 years ago
6

PLEASE HELP ME!!! Find the vertex of f(x)=x^2+2x+3 and show your work

Mathematics
1 answer:
belka [17]3 years ago
5 0

Answer:

The vertex is the point (-1,2)

Step-by-step explanation:

we have

f(x)=x^{2}+2x+3

Convert into vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

f(x)-3=x^{2}+2x

Complete the square. Remember to balance the equation by adding the same constants to each side.

f(x)-3+1=x^{2}+2x+1

f(x)-2=x^{2}+2x+1

Rewrite as perfect squares

f(x)-2=(x+1)^{2}

f(x)=(x+1)^{2}+2 ----> equation in vertex form

The vertex is the point (-1,2)

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2 years ago
Need help with this question
kumpel [21]

Answer:

B

Step-by-step explanation:

The problem wants you to PLUG IN x into the correct equation.

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f(3) means 3 equals x

For example g(9) means 9 = x and f(3/5) means 3/5 = x and so on.

2) Now that you know x equals two numbers -1 and 3 you have to plug them into a equation.

3) Which equation do you plug it in you may ask? You must plug in -1 into x^2 +3 BECAUSE the condition next to it says you can only plug in numbers to x^2+3 greater than or equal to -1 and less than 2. Therefore, you can plug in -1 to this equation.

-1^2 +3 = <u>4</u>

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1, for x >= 2 because 3 is certainly bigger than 2.

This means any number greater than or equal to 2 has to be 1.

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Answer:

B. The horizontal cross-sections of the prisms at the same height have the same area.

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<em>Notice that the cone and the pyramid have the same volume. This is important. </em>

This follows the <em>Cavalieri's principle</em> that, for the case of 3 dimensions, as the present case, it states, roughly, that if we have two bodies like the cone and the pyramid, and if we have parallel planes crossing each section, and we always have the same area, these two bodies have the same volume.

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B. The horizontal cross-sections of the prisms at the same height have the same area.

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