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Write the equation of the parabola that passes through the points (1,0)(1,0), (2,0)(2,0), (3,−6)(3,-6). Write your answer in the form y=a(x–p)(x–q)y=a(x–p)(x–q), where aa, pp, and qq are integers, decimals, or simplified fractions.

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Q. Write the equation of the parabola that passes through the points (1,0)(1,0), (2,0)(2,0), (3,−6)(3,-6). Write your answer in the form y=a(x–p)(x–q)y=a(x–p)(x–q), where aa, pp, and qq are integers, decimals, or simplified fractions.
  1. Identify pp and qq: Identify the values of pp and qq from the given points (1,0)(1,0) and (2,0)(2,0) which are the x-intercepts of the parabola.
  2. Write general form: Write the general form of the equation using the values of pp and qq.
  3. Substitute point (3,−6)(3, -6): Substitute the point (3,−6)(3, -6) into the equation to find the value of aa.
  4. Write final equation: Write the final equation of the parabola using the found value of aa.

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