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Write the equation of the parabola that passes through the points (−2,0)(-2,0), (−1,4)(-1,4), (1,0)(1,0) 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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Write a quadratic function from its x-intercepts and another pointright chevron icon

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Q. Write the equation of the parabola that passes through the points (−2,0)(-2,0), (−1,4)(-1,4), (1,0)(1,0) 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 Points: Identify the values of pp and qq from the given points. The points (−2,0)(-2, 0) and (1,0)(1, 0) are x-intercepts, so p=−2p = -2 and q=1q = 1.
  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=−2p = -2 and q=1q = 1, we get y=a(x+2)(x−1)y = a(x + 2)(x - 1).
  3. Find Value of a: Use the point (−1,4)(-1, 4) to find the value of aa. Substitute x=−1x = -1 and y=4y = 4 into the equation: 4=a(−1+2)(−1−1)4 = a(-1 + 2)(-1 - 1).
  4. Simplify and Solve: Simplify and solve for aa: 4=a(1)(−2)4 = a(1)(-2), 4=−2a4 = -2a, a=−2a = -2.

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