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Find the equation to the parabola, whose axis parallel to the y -axis and which passes through the points (0,4),(1,9) and (4,5) is

Options

  1. Ay=-x^2+x+4
  2. By=-x^2+x+1
  3. Cy= -19 12 x^2+ 79 12 x+4
  4. Dy= -19 12 x^2+ 89 12 +1

Correct answer

C. y= -19 12 x^2+ 79 12 x+4

Step-by-step solution

The equation of parabola parallel to y -axis is y=A x^2+B x+C ...(i) The point (0,4),(1,9) and (4,5) lies on Eq. (i). Then, 4=0+0+C C=4 ...(ii) 9=A+B+C or 9=A+B+4 ( C=4)A+B=5 ...(iii) and 5=16 A+4 B+C ( C=4) or 5=16 A+4 B+4 16 A+4 B=14 A+B= 1 4 ...(iv) Solving Eqs. (iii) and (iv), we get A= -19 12 , B= 79 12 ...(v) Substituting the values of A, B and C from Eqs. (ii) and (v) in Eq. (i), then equation of parabola is y= -19 12 x^2+ 79 12 x+4

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