Write the equation of the parabola that passes through the points (−2,28), (−1,0), and (5,0). 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 (−2,28), (−1,0), and (5,0). 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: We have the points (−2,28), (−1,0), and (5,0). The points (−1,0) and (5,0) are the x-intercepts of the parabola, so they give us the values of p and q directly.p=−1 and q=5.
Write Parabola Equation: Now we can write the equation of the parabola in the form y=a(x−p)(x−q) using the values of p and q we found.y=a(x−(−1))(x−5)y=a(x+1)(x−5)
Find Value of a: Next, we need to find the value of a. We will use the point (−2,28) to do this. Substitute x=−2 and y=28 into the equation y=a(x+1)(x−5).28=a(−2+1)(−2−5)
Simplify and Solve: Simplify the equation to solve for a.28=a(−1)(−7)28=7aa=728a=4
Final Equation: Now that we have found a=4, we can write the final equation of the parabola.y=4(x+1)(x−5)
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