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Write the equation of the parabola that passes through the points (−5,0)(-5,0), (−2,−30)(-2,-30), (3,0)(3,0) 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 (−5,0)(-5,0), (−2,−30)(-2,-30), (3,0)(3,0) 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 (−5,0)(-5,0) and (3,0)(3,0). These points indicate where the parabola crosses the x-axis, so p=−5p = -5 and q=3q = 3.
  2. Write parabola equation: Write the equation of the parabola using the form y=a(x−p)(x−q)y = a(x - p)(x - q). Substituting p=−5p = -5 and q=3q = 3, we get y=a(x+5)(x−3)y = a(x + 5)(x - 3).
  3. Find value of aa: Use the point (−2,−30)(-2, -30) to find the value of aa. Substitute x=−2x = -2 and y=−30y = -30 into the equation: −30=a(−2+5)(−2−3)-30 = a(-2 + 5)(-2 - 3).
  4. Solve for aa: Simplify and solve for aa: −30=a(3)(−5)-30 = a(3)(-5), −30=−15a-30 = -15a, a=2a = 2.

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