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RUDIKE [14]
2 years ago
11

Write the equation of a quadratic function that contains the points (1,21), (2,18), and (-1,9)

Mathematics
1 answer:
Colt1911 [192]2 years ago
7 0

Answer:

The equation of a quadratic function that contains the points (1, 21), (2,18) and (-1, 9) is y = -3\cdot x^{2}+6\cdot x +18.

Step-by-step explanation:

A quadratic function is a second order polynomial of the form:

y = a\cdot x^{2}+b\cdot x + c (1)

Where:

x - Independent variable.

y - Dependent variable.

a, b, c - Coefficients.

From Algebra we understand that a second order polynomial is determined by knowing three distinct points. If we know that (x_{1}, y_{1}) = (1, 21), (x_{2},y_{2}) = (2,18) and (x_{3}, y_{3}) = (-1, 9), then we construct the following system of linear equations:

a+b+c = 21 (2)

4\cdot a + 2\cdot b + c = 18 (3)

a - b + c = 9 (4)

By algebraic means, the solution of the system is:

a = -3, b = 6, c = 18

Therefore, the equation of a quadratic function that contains the points (1, 21), (2,18) and (-1, 9) is y = -3\cdot x^{2}+6\cdot x +18.

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the diameter of a piston for an automobile is 3 11/16in with tolerence of 1/64in. find the upper and lower limits of the pistons
padilas [110]

Upper Tolerance

Remark

The 11/16 is the only thing that will be affected. The three won't go up or down when we add 1/64 so we should just work with the 11/16. We need only add 11/16 and 1/64 together to see what the upper range is. Later on we can add 3 into the mix.

Solution

<u>Upper Limit</u>

\dfrac{11}{16} +  \dfrac{1}{64}

Now change the 11/16 into 64. Multiply numerator and denominator or 11/16 by 4

\dfrac{11*4}{16*4} +  \dfrac{1}{64}

\dfrac{11*4}{16*4} +  \dfrac{1}{64} Which results in

\dfrac{44}{64} +  \dfrac{1}{64}

With a final result for the fractions of 45/64

So the upper tolerance = 3 45/64

<u>Lower Tolerance</u>

Just follow the same steps as you did for the upper tolerance except you subtract 1/64 like this.

\dfrac{11}{16} - \dfrac{1}{64}

Your answer should be 3 and 43/64


4 0
3 years ago
Find a 5% commission for $18,000 in sales?
weeeeeb [17]
5% of 18,000 is 900 , hope this helps.
3 0
2 years ago
How do I factorize 2x-6
LiRa [457]
<span> The answer
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Suppose that there are two types of tickets to a show: advance and same-day. The combined cost of one advance ticket and one sam
avanturin [10]
Let "a" and "s" represent the costs of advance and same-day tickets, respectively. Your problem statement gives you two relations.
.. a + s = 35 . . . . . the combined cost of one of each is 35
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There are many ways to solve these equations. You've probably been introduced to "substitution" and "elimination" (or "addition"). Using substitution for "a", we have
.. a = 35 -s
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.. a = 35 -15 = 20

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The price of a same-day ticket was 15.
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3 years ago
how high up on a building will 15 foot ladder reach if the foot of the ladder is placed 5 feet from the building? (be sure to in
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