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Write the equation of the parabola that passes through the points (−5,−36)(-5,-36), (−3,0)(-3,0), (−2,0)(-2,0). 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 (−5,−36)(-5,-36), (−3,0)(-3,0), (−2,0)(-2,0). 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 x-intercepts: Identify the x-intercepts from the given points. The x-intercepts are where y=0y=0. Points: (−3,0)(-3,0) and (−2,0)(-2,0) are x-intercepts.
  2. Set pp and qq: Set pp and qq as the xx-intercepts. p=−3p = -3, q=−2q = -2. Write the equation in the form y=a(x−p)(x−q)y = a(x - p)(x - q). y=a(x+3)(x+2)y = a(x + 3)(x + 2).
  3. Use point to find 'a': Use the point (−5,−36)(-5,-36) to find the value of 'a'. Substitute x=−5x = -5 and y=−36y = -36 into the equation. −36=a(−5+3)(−5+2)-36 = a(-5 + 3)(-5 + 2). −36=a(−2)(−3)-36 = a(-2)(-3). −36=6a-36 = 6a.
  4. Solve for 'a': Solve for 'a'. −36=6a-36 = 6a. Divide both sides by 66. a=−6a = -6.
  5. Write final equation: Write the final equation using the values of aa, pp, and qq. y=−6(x+3)(x+2)y = -6(x + 3)(x + 2).

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