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satela [25.4K]
3 years ago
8

Parabola passes through the points (0,5), (1,4), and (2,5). What function does the graph represent?

Mathematics
1 answer:
AfilCa [17]3 years ago
7 0

Answer:

x^2 - 2x + 5 = 0.

Step-by-step explanation:

The (0, 5) is the point where the parabola passes through the y axis (where x = 0), so we can write the equation as

y = ax^2 + bx + 5   where a and b are constants to be found.

Also, since (1, 4) and (2, 5) are points on the curve, substituting, we have the system:

a(1)^2 + 1b + 5 = 4

a(2)^2 + 2b + 5 = 5

Simplify these 2 equations:

a  + b  =  -1  .................(1)

4a + 2b = 0..................(2)

Multiply the first equation by -2:

-2a - 2b = 2 .................(3)

Add (2) + (3):

2a = 2

a = 1.

Substitute a = 1 into (2):-

4*1 + 2b = 0

2b = -4

b = -2.

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Answer:

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You can notice the pattern. If dad walks 3 steps, son walks 5. If dad walks another 3, son walks another 5. And so on. This means dad walks 12 steps when the sin walks 20 steps.

Step-by-step explanation:

The ratio is 3:5. This means dad wlaks 3 steps so son must walk 5 steps basically. So.......... You can now create the table. Y I just have to multiply or divide each side ( of the colon:) so. Whatever you do to one side, you do to the other side. If you x3 on one side, you do it to other. Same goes for division. In the 'table' I did above, I x2 to get 6 and 10. Then I took the 3 and the 5 again and timsed those by 3. You can also change the 6 and the 10. So:

3:5

Then x2

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Then I take the top layer (you can either choose to change the top layer, or layer above as long as you do the same thing to each side. Remember, only x and ÷. No + or-.) and I x3

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Then I could take 9 and 15 and x5

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It's crazy that all these. Ratios mena the same thing! 45 steps from dad would take the son 75 steps. You can also divide the last ratio of 45:75 to find the one you started with, 3:5.

So you get the idea.

It is probably best to do what I did in the table in the answer part because I did a pattern. Take the top layer, and x2, then x3, then x4, ect. Rather then doing random things.

5 0
4 years ago
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Neko [114]

Answer:

Step-by-step explanation:

this one is tricky    so b/c the lines are at 90 degees we know that the arcs are similar so set up the parts of the arcs equal to 360 degrees

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see each part of the circle ?

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Irina-Kira [14]

Answer:

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Step-by-step explanation:

You want x such that ...

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kipiarov [429]
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4 years ago
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Answer:

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Step-by-step explanation:

I hope this helps

Have an amazing day!

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