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Find a polynomial function whose graph passes through (-1,-4) (0,1),(1,4) and (2,11)

User CMPalmer
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The points that the graph line passes through on the graph are (- 1, - 4), (0, 1), (1, 4) and (2, 11)

The equation of the polynomial can be expressed in the slope intercept form which is expressed as

y = mx + c

where

m represents slope

c represents y intercept

The formula for determining slope is expressed as

m = (y2 - y1)/(x2 - x1)

Considering the first two points,

x1 = - 1, y1 = - 4

x2 = 0, y2 = 1

m = (1 - - 4)/(0 - - 1) = (1 + 4)/(0 + 1) = 5/1

m = 5

We would find the y intercept by substituting m = 5, x = - 1 and y = - 4 into the equation. It becomes

- 4 = 5 * - 1 + c

- 4 = - 5 + c

c = - 4 + 5

c = 1

By substituting m = 5 and c = 1 into the slope intercept equation, the equation of the line would be

y = 5x + 1

We can check by substituting x = 2 and y = 11 from the last point into the equation. It becomes

11 = 5 * 2 + 1

11 = 11

To express it as a function, we would replace y with f(x). Thus, the function whose graph passes through (-1,-4) (0,1),(1,4) and (2,11)​ is

f(x) = 5x + 1

User Dbernard
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