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Find the quadratic equation of the form y=ax^ 2 +bx+c, whose graph passes through the points (2, 3) ( -2,7)and (1, - 2) .

1 Answer

4 votes

Answer:

y = 2x^2 -x -3

Explanation:

It can be convenient to use the quadratic regression capability of a graphing calculator or spreadsheet. That's what we did in the attachment.

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Fill in the given points in the equation to find three linear equations in a, b, c.

3 = a(2^2) +b(2) +c

7 = a(-2)^2 +b(-2) +c

-2 = a(1^2) +b(1) +c

Subtracting the last equation from the first two gives ...

(3) -(-2) = (4a +2b +c) -(a +b +c) ⇒ 5 = 3a +b

(7) -(-2) = (4a -2b +c) -(a +b +c) ⇒ 9 = 3a -3b . . . . . [eq5]

Subtracting the second of these equations from the first gives ...

(5) -(9) = (3a +b) -(3a -3b) ⇒ -4 = 4b

b = -1

Dividing [eq5] by 3 gives ...

3 = a - b

3 = a -(-1)

2 = a

Using the original 3rd equation, we have ...

-2 = a +b +c

-2 = 2 +(-1) + c

-3 = c . . . . . . . . subtract 1

The desired quadratic is ...

y = 2x^2 -x -3

Find the quadratic equation of the form y=ax^ 2 +bx+c, whose graph passes through-example-1
User Bstenzel
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