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lilavasa [31]
3 years ago
7

Given the x-intercepts for the graph of a quadratic function, write a possible formula for the quadratic function, in

Mathematics
1 answer:
eduard3 years ago
5 0

Answer:

Step-by-step explanation:

x-intercepts are SOLUTIONS to a quadratic whereas when you put those solutions into factor form (in a set of parenthesis), you have the FACTORS of the quadratic.  They are the same thing generally, they are just written in different forms.  For example, if a solution to a quadratic is x = 3, it has been understood that x = 3 when y = 0. Therefore, if x - 3 = y and y = 0, then x - 3 = 0.  Solving that for x, you get x = 3.  That factor of x = 3 is (x - 3).

Following that logic, for a:

If the x intercepts are x = 0 and x = 3, it is understood that x + 0 = 0 so x = 0 and the factor is (x + 0) (it could also be x - 0 since adding 0 is the same as subtracting 0); if x = 3 it is understood that x - 3 = 0 and the factor is (x - 3).

For b:

If the x-intercepts are x = -1 and x = 1, then originally the factors were (x + 1) and (x - 1).  Again, set each of those equal to 0 and solve for x (THE X-INTERCEPT EXISTS WHERE Y = 0!)

For c:

If the x-intercepts are x = -5 and x = 10, then originally the factors were (x + 5) and (x - 10).

For d:

If the x-intercept is a fraction, do the same thing:

x = 1/2 so

x - 1/2 = 0 Now multiply both the x and the 1/2 by a 2 to get the factor (2x - 1) and the other factor from x = 4 is (x - 4)

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Solve for m and n<br> I been stuck on this question for an hour
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m = 10 , n = 5\sqrt{2}

Step-by-step explanation:

using the cosine and tangent ratio in the right triangle and the exact values

cos45° = \frac{1}{\sqrt{2} } and tan45° = 1 , then

cos45° = \frac{adjacent}{hypotenuse} = \frac{5\sqrt{2} }{m} = \frac{1}{\sqrt{2} } ( cross- multiply )

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-----------------------------------------

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3 0
2 years ago
What is the volume of the prism?
mezya [45]

Answer:

40 \frac{5}{8} cm^{3}

Step-by-step explanation:

The figure is a rectangular prism, so the formula would be Volume = length x width x height.

length =  6 \frac{1}{2} cm

width  =  2 \frac{1}{2} cm

height  =  2 \frac{1}{2} cm

If you plug everything you have in the problem into the volume equation, you would get : Volume = 6 \frac{1}{2} cm x 2 \frac{1}{2} cm x 2 \frac{1}{2} cm.

Without a calculator, I would first turn the mixed numbers into improper fractions.

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Volume = \frac{13}{2} x  \frac{5}{2} x  \frac{5}{2}

When you multiply everything together you should get \frac{325}{8}.

As a mixed number, that would be 40 \frac{5}{8} cm^{3}.

7 0
3 years ago
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