Write the equation of the parabola that passes through the points (-3,24), (-2,0), and (3,0). Write your answer in the form y = a(x - p)(x - q), where a, p, and q are integers, decimals, or simplified fractions. ______

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Write the equation of the parabola that passes through the points (-3,24), (-2,0), and (3,0). Write your answer in the form y = a(x - p)(x - q), where a, p, and q are integers, decimals, or simplified fractions.   ______

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Identify x-intercepts: We have the points (-3,24), (-2,0), and (3,0). The points (-2,0) and (3,0) are the x-intercepts of the parabola, so they give us the values of p and q directly. Therefore, p = -2 and q = 3.Write parabola equation: Using the values of p and q, we can write the equation of the parabola in the form y = a(x - p)(x - q). Substituting -2 for p and 3 for q, we get y = a(x + 2)(x - 3).Find value of a: Now we need to find the value of a. We can use the point (-3,24) to do this. Substituting -3 for x and 24 for y into the equation y = a(x + 2)(x - 3), we get 24 = a(-3 + 2)(-3 - 3).Solve for a: Solving the equation 24 = a(-1)(-6), we find that 24 = 6a, which means that a = 24 / 6 = 4.Final equation of parabola: Now that we have found a = 4, we can write the final equation of the parabola. Substituting 4 for a, -2 for p, and 3 for q into the equation y = a(x - p)(x - q), we get y = 4(x + 2)(x - 3).

Write the equation of the parabola that passes through the points $(-3,24$ ), $(-2,0$ ), and $(3,0$ ). Write your answer in the form $y = a(x - p)(x - q)$ , where $a$ , $p$ , and $q$ are integers, decimals, or simplified fractions.

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Write the equation of the parabola that passes through the points (−3,24(-3,24(−3,24), (−2,0(-2,0(−2,0), and (3,0(3,0(3,0). Write your answer in the form y=a(x−p)(x−q)y = a(x - p)(x - q)y=a(x−p)(x−q), where aaa, ppp, and qqq are integers, decimals, or simplified fractions.

Write the equation of the parabola that passes through the points $(-3,24$ ), $(-2,0$ ), and $(3,0$ ). Write your answer in the form $y = a(x - p)(x - q)$ , where $a$ , $p$ , and $q$ are integers, decimals, or simplified fractions.