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Write the equation of the parabola shown in the graph. (−3,0)(−2,−6)(1,0)(-3,0)(-2,-6)(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 shown in the graph. (−3,0)(−2,−6)(1,0)(-3,0)(-2,-6)(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 (−3,0)(-3,0) and (1,0)(1,0). These points indicate where the parabola crosses the x-axis, so p=−3p = -3 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=−3p = -3 and q=1q = 1, we get y=a(x+3)(x−1)y = a(x + 3)(x - 1).
  3. Find value of aa: Use the point (−2,−6)(-2, -6) to find the value of aa. Substitute x=−2x = -2 and y=−6y = -6 into the equation y=a(x+3)(x−1)y = a(x + 3)(x - 1).
  4. Calculate aa: Calculate aa using the substituted values: −6=a(−2+3)(−2−1)-6 = a(-2 + 3)(-2 - 1), −6=a(1)(−3)-6 = a(1)(-3), −6=−3a-6 = -3a, a=2a = 2.

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