Write the equation of the parabola that passes through the points shown in the table. (−2,0)(4,−24)(6,0) Write your answer in the form y=a(x–p)(x–q), where a, p, and q are integers, decimals, or simplified fractions
Q. Write the equation of the parabola that passes through the points shown in the table. (−2,0)(4,−24)(6,0) Write your answer in the form y=a(x–p)(x–q), where a, p, and q are integers, decimals, or simplified fractions
Identify x-intercepts: Identify the x-intercepts from the given points. Points (−2,0) and (6,0) are x-intercepts, so p=−2 and q=6.
Write parabola equation: Write the equation of the parabola using the form y=a(x−p)(x−q). Substituting p and q, we get y=a(x+2)(x−6).
Find value of a: Use the point (4,−24) to find the value of a. Substitute x=4 and y=−24 into the equation: −24=a(4+2)(4−6).
Solve for a: Simplify and solve for a: −24=a(6)(−2), −24=−12a, a=2.
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