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IrinaK [193]
3 years ago
15

Form quadratic functions given the following information: Zeroes at 4 and –2, f(0)=4

Mathematics
1 answer:
laila [671]3 years ago
5 0

Answer:

f(x)=-0.5x^2+x+4

Step-by-step explanation:

we know that

A quadratic function in factored form is equal to

f(x)=a(x-x_1)(x-x_2)

where

a is the leading coefficient

x_1 and x_2 are the zeroes of the function

substitute the given values

f(x)=a(x-4)(x+2)

Find the value of a

Remember that

For x=0 ----> f(0)=4

substitute

4=a(0-4)(0+2)

4=a(-8)\\a=-0.5

so

f(x)=-0.5(x-4)(x+2)

f(x)=-0.5(x^2+2x-4x-8)

f(x)=-0.5(x^2-2x-8)

f(x)=-0.5x^2+x+4

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3 years ago
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How would I find a? What formula would I use?
xenn [34]

Answer:

  You can use either of the following to find "a":

  • Pythagorean theorem
  • Law of Cosines

Step-by-step explanation:

It looks like you have an isosceles trapezoid with one base 12.6 ft and a height of 15 ft.

I find it reasonably convenient to find the length of x using the sine of the 70° angle:

  x = (15 ft)/sin(70°)

  x ≈ 15.96 ft

That is not what you asked, but this value is sufficiently different from what is marked on your diagram, that I thought it might be helpful.

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Consider the diagram below. The relation between DE and AE can be written as ...

  DE/AE = tan(70°)

  AE = DE/tan(70°) = DE·tan(20°)

  AE = 15·tan(20°) ≈ 5.459554

Then the length EC is ...

  EC = AC - AE

  EC = 6.3 - DE·tan(20°) ≈ 0.840446

Now, we can find DC using the Pythagorean theorem:

  DC² = DE² + EC²

  DC = √(15² +0.840446²) ≈ 15.023527

  a ≈ 15.02 ft

_____

You can also make use of the Law of Cosines and the lengths x=AD and AC to find "a". (Do not round intermediate values from calculations.)

  DC² = AD² + AC² - 2·AD·AC·cos(A)

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3 0
3 years ago
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laila [671]

Answer:

1080 in^2

Step-by-step explanation:

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When a = 6 and b = 22, c = 33. If c varies directly with b and inversely with a, which equation models the situation?
deff fn [24]

Answer:

c= 9b/a

Step-by-step explanation:

The statement "y varies directly as x," means that when x increases, y increases by the same factor. The statement "y varies inversely as x means that when x increases, ydecreases by the same factor.

Then, we can say that:

c ∝ b, thus c= kb and c = k/a.

Using both equations we have that:

c= kb/a

Given that a=6, b=22 and c=33 we have that:

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Solving for k:

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