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Mice21 [21]
3 years ago
13

Which is the graph of f(x) = x2 – 2x + 3?

Mathematics
1 answer:
BaLLatris [955]3 years ago
7 0

Answer:

Step-by-step explanation:

We cannot factor this function out which tells us that there are no zeros. The graph backs this up because we can see that there are none. The easiest way to graph this would start by plugging in points and making a table for yourself.

Lets start by plugging in -1.

(-1)^2-2(-1)+3 =6, this means we have a point at (-1,6).

Now lets plug in 0.

(0)^2-2(0)+3= 3 (0,3)

For plugging in 1

(1)^2-2(1)+3=2 (1,2) (this happens to be the vertex)

And lastly lets plug in 2

(2)^2-2(2)+3=3 (2,3)

Depending on how many points are needed, keep plugging in numbers like we did above.

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3 years ago
Which equations and/or functions represent the graphed line? Select three options.
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Answer:

f(x) = 0.5x + 2

f(x) = 1/2x + 2

y - 3 = 1/2(x - 2)

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Step-by-step explanation:

In the figure attached, the graphed line is shown.

The missing options are:

<em>f(x) = 0.2x - 4 </em>

<em>f(x) = 0.5x + 2  </em>

<em> f(x) = 1/2x + 2 </em>

<em> y – 3 = 1/2(x – 2) </em>

<em> y – 1 = 0.5(x + 2)</em>

From the picture, we can see that points (0, 2) and (2, 3) are on the line. Then, the slope of the line is:

m = (3 - 2)/(2 - 0) = 1/2 = 0.5

The y-intercept is (0, 2), or b = 2

Therefore, in the slope y-intercept form, the equation is:

f(x) = mx + b

f(x) = 1/2x + 2 = 0.5x + 2

In the point-slope form, the equations is:

y - y1 = m(x - x1)

y - 3 = 1/2(x - 2)

Using point (-2, 1), in the point-slope form, the equation is:

y - y1 = m(x - x1)

y - 1 = 0.5(x + 2)

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In a tape diagram, each of the lengths represents a fixed quantity of something.

Let's suppose that each one of these lengths represents a distance d.

We also know that the expert trail is 750 meters longer than the beginner one.

And in the tape diagram, the expert trail has 3 more lengths than the beginner trail, then we must have that the difference in distance must be equivalent with the difference in lengths.

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Then each length in the tape diagram represents 250m

With this we can find the length of each trail.

The beginner trail has 1 length, then it is 1*250m = 250 meters long.

The expert trail has 4 lengths, then it is 4*250m = 1000 meters long.

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