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Write the equation of the parabola that passes through the points (−10,14)(-10,14), (−8,0)(-8,0), (−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 (−10,14)(-10,14), (−8,0)(-8,0), (−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 values of pp and qq: Identify the values of pp and qq from the given points. The points (−8,0)(-8, 0) and (−3,0)(-3, 0) are xx-intercepts, so p=−8p = -8 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=−8p = -8 and q=−3q = -3, we get y=a(x+8)(x+3)y = a(x + 8)(x + 3).
  3. Use point to find aa: Use the point (−10,14)(-10, 14) to find the value of aa. Substitute x=−10x = -10 and y=14y = 14 into the equation: 14=a(−10+8)(−10+3)14 = a(-10 + 8)(-10 + 3).
  4. Simplify and solve for aa: Simplify and solve for aa: 14=a(−2)(−7)=14a14 = a(-2)(-7) = 14a. Divide both sides by 1414 to find aa: a=1a = 1.
  5. Write final parabola equation: Write the final equation of the parabola using the values of aa, pp, and qq. Substitute a=1a = 1, p=−8p = -8, and q=−3q = -3 into y=a(x−p)(x−q)y = a(x - p)(x - q) to get y=1(x+8)(x+3)y = 1(x + 8)(x + 3).

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