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Find a polynomial function whose graph passes through (7,13), (9,- 11), and (0,3).

1 Answer

5 votes

Explanation:

I am going to assume this is a quadratic so


f(x) = {ax}^(2) + bx + c

When 3 is c


{ax}^(2) + bx + 3

When x is 7,


a( {7}^(2) ) + b(7) + 3 = 13


49a + 7b = 10

When x is 9,


a(9) {}^(2) + 9b + 3 = - 11


81a + 9b = - 14

We have two system, let's eliminate the b variable by multiplying the second system by


(7)/(9)


63a + 7b = - (98)/(9)

Bring down the first system


49a + 7b = 10

Subtract the two system,


14a = ( - 188)/(9)


a = - (94)/(63)

Plugging in a, we will eventually get


b = (748)/(63)

So our quadratic is


- (94)/(63) {x}^(2) + (748)/(63) x + 3

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