Write the equation of the parabola that passes through the points (2,24), (4,0), and (-2,0). 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 (2,24), (4,0), and (-2,0). 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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Find p and q: We have the points (2,24), (4,0), and (-2,0). The points (4, 0) and (-2, 0) are the x-intercepts of the parabola, so they give us the values of p and q directly. p = 4 and q = -2.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. Substitute 4 for p and -2 for q into the equation y = a(x - p)(x - q). y = a(x - 4)(x - (-2)) y = a(x - 4)(x + 2)Find value of a: Next, we need to find the value of a. We can use the point (2,24) to do this, as this point lies on the parabola. Substitute 2 for x and 24 for y into the equation y = a(x - 4)(x + 2). 24 = a(2 - 4)(2 + 2)Solve for a: Now we solve the equation to find the value of a. 24 = a(-2)(4) 24 = -8a a = 24 / -8 a = -3Final equation of parabola: We have found that a = -3. Now we can write the final equation of the parabola using the values of a, p, and q. Substitute -3 for a, 4 for p, and -2 for q into the equation y = a(x - p)(x - q). y = -3(x - 4)(x + 2)

Write the equation of the parabola that passes through the points $(2,24)$ , $(4,0)$ , and $(-2,0)$ . 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 (2,24)(2,24)(2,24), (4,0)(4,0)(4,0), and (−2,0)(-2,0)(−2,0). 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 $(2,24)$ , $(4,0)$ , and $(-2,0)$ . Write your answer in the form $y = a(x - p)(x - q)$ , where $a$ , $p$ , and $q$ are integers, decimals, or simplified fractions.