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Write the equation of the parabola shown in the graph. (−2,0)(-2,0)(−1,8)(-1,8)(1,0)(1,0). Write the equation of the parabola shown in the graph. 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 shown in the graph. (−2,0)(-2,0)(−1,8)(-1,8)(1,0)(1,0). Write the equation of the parabola shown in the graph. 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 and vertex: Identify the x-intercepts and vertex from the given points (−2,0)(-2,0), (−1,8)(-1,8), (1,0)(1,0). The x-intercepts are at (−2,0)(-2,0) and (1,0)(1,0), so p=−2p = -2 and q=1q = 1.
  2. Write equation in standard form: Write the equation in 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 using vertex: Use the vertex point (−1,8)(-1,8) to find the value of aa. Substitute x=−1x = -1 and y=8y = 8 into the equation: 8=a(−1+2)(−1−1)8 = a(-1 + 2)(-1 - 1).
  4. Simplify and solve for aa: Simplify and solve for aa: 8=a(1)(−2)8 = a(1)(-2), 8=−2a8 = -2a, a=−4a = -4.

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