Shelley
12 grade student

let (0,3) and (1,9)and (-1,1) be given points in a parablola. Determine a b and c



Hi Shelley,

The general form of a parabola is

y = a x 2 + b x + c

If (0,3) is on the parabola then the equation must be true when x = 0 and y = 3. Substituting these values into the equation gives

3 = a0 2 + b0 + c = c Thus c = 3 and hence the equation is y = a x 2 + b x + 3

Simularily if (1,9) and (-1,1) are on the parabola then

9 = a1 2 + b1 + 3 = a + b + 3 and 1 = a(-1) 2 + b(-1) + 3 = a - b + 3

Solve this pair of equations for a and b.

Cheers,
Penny

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