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sertanlavr [38]
3 years ago
13

Write the equation of the parabola that has the vertex at point (5,0) and passes through the point (7,−2).

Mathematics
1 answer:
lord [1]3 years ago
3 0

The vertex form of the equation of a parabola is

                     f(x) = a( x − h)^2 + k

where (h,k) is the vertex of the parabola. In this case, we are given that      (h,k) = (5,0). Hence,

                     f(x) = a( x − 5)^2 + 0

                           =a( x − 5)^2

Since we also know the parabola passes through the point (7,−2), we can solve for a because we know that f(7) = −2.

                        a( 7 − 5)^2 = -2

                           a(2)^2 = -2

                              4a = -2

                               a = -1/2

Thus, the given parabola has equation

                      f(x) = -1/2(x − 5)^2

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Is -3 a natural number a whole number a integer a rational number or irrational number
BaLLatris [955]

Answer:

-3 is a rational integer.

Step-by-step explanation:

An integer is a superset of the whole numbers that includes the negated values as well as 0.

A rational number is simply anything that can be expressed as a fraction.

-3 is by these definitions, a negated 3, and any non fractional number can be expressed as a fraction.

-3 is not a natural number, as that is the set of numbers {1, 2, 3, 4, 5, ... etc} and -3 is not a whole number, as that is the set of numbers {0, 1, 2, 3, 4, ... etc}.

And -3 is also not an irrational number since it can be expressed as a fraction.

Thus, -3 is a rational integer.

Cheers.

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Let's try to divide the sentence into multiple parts and then combine it one by one to make it easier to understand. 

1. True
2 times y and 6                                                          -------->(2y+6)
the square of the sum of "2 times y and 6"             -------->(2y+6)^2
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2. True
the difference of x and 7                            -------->(x-7)
9 and x                                                         -------->(9 + x)
2 times the product of the sum of
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3. True
difference of 5 times x and 3   -------->(5x-3)
the square of the difference of 5 times x and 3------->(5x-3)^2

4. False
The description should be: the product of 7 and the square of x
the product of 7 and x                        -------->(7x)
the square of the product of 7 and x -------->(7x)^2

5. True
This one should be clear as it was one sentences
the sum of y squared(y^2) and three times y(3y) minus 4-------->y^2+ 3y -4

6. False
The description should be: the product of 5 and 8 times the square of x plus the sum of 20x and 8
the sum of 20x and 8                -------->20x+8
8 plus the square of x plus the sum of 20x and 8-------->8+ x^2 +20x+8
the product of 5 and....                ------->(5)(........
the product of 5 and
8 plus the square of x plus the sum of 20x and 8---->(5)(8+ x^2 +20x+8)
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