Which function, when graphed, would contain all the points in the table below?

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alissa3329 alissa3329

16-04-2019
Mathematics

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Which function, when graphed, would contain all the points in the table below?

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vaarun5 vaarun5 · Answer 1 · 2019-04-16T23:38:54+02:00

vaarun5 vaarun5

16-04-2019

This is an interesting function but it seems to be:

f(x) = Square Root( -x)

The -x would make all the current x values positive.

Then taking the square root of these values would give you the y value.

Square Root(-0) = 0

Square Root(-(-1)) = 1

Square Root(-(-4)) = 2

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mahendravt mahendravt · Answer 2 · 2022-08-11T09:33:36+02:00

The required function for the given points is y = -1/6 x² - 7/6x.

Whats are quadratic function?

In algebra, a quadratic function is one of the form

f(x) = ax² + bx + c

where a,b,c are numbers with not equal to zero.

Now, let us suppose y be the function of the given points in the table

so, y = f(x) = ax² + bx + c

Putting the values of x and y from the table in function y we get,

y = 0 = a0² + 0b + c

⇒ c = 0

y = 1 = a (-1)² + b(-1) + 0 [∵ c = 0]

⇒ a-b = 1 ...(i)

y = 2 = a (-4)² + (-4)b + c

⇒ 16a - 4b + c = 2

simplyfying,

⇒ 8a - 2b = 1 ...(ii)

Solving eq(i) and (ii). we get

a = -1/6

b = -7/6

Putting the values of a,b,c in y. We get

y = (-1/6)x² + (-7/6)x + 0

⇒ y = -1/6 x² - 7/6x

Hence,the required function for the given points is y = -1/6 x² - 7/6x.

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