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Write the equation of the parabola that passes through the points (−4,0)(-4,0), (−3,4)(-3,4), (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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Full solution

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

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