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Write the equation of the parabola shown in the graph. (−5,4)(−4,0)(−3,0)(-5,4)(-4,0)(-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 shown in the graph. (−5,4)(−4,0)(−3,0)(-5,4)(-4,0)(-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 pp and qq: Identify the values of pp and qq from the given points where the parabola crosses the x-axis. Points (−4,0)(-4,0) and (−3,0)(-3,0) are x-intercepts, so p=−4p = -4 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). Substitute −4-4 for pp and −3-3 for qq: y=a(x+4)(x+3)y = a(x + 4)(x + 3).
  3. Find value of aa: Use the point (−5,4)(-5, 4) to find the value of aa. Substitute −5-5 for xx and 44 for yy in the equation: 4=a(−5+4)(−5+3)4 = a(-5 + 4)(-5 + 3).
  4. Solve for aa: Simplify and solve for aa: 4=a(−1)(−2)4 = a(-1)(-2), 4=2a4 = 2a, a=2a = 2.
  5. Final parabola equation: Write the final equation of the parabola substituting a=2a = 2, p=−4p = -4, and q=−3q = -3 into y=a(x−p)(x−q)y = a(x - p)(x - q): y=2(x+4)(x+3)y = 2(x + 4)(x + 3).

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