Write the equation of the parabola that passes through the points (1,0), (2,0), and (3,–16). 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 (1,0), (2,0), and (3,–16). 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 are given three points through which the parabola passes: (1,0), (2,0), and (3,–16). The points (1,0) and (2,0) are the x-intercepts of the parabola, which means they correspond to the values of p and q in the equation y = a(x – p)(x – q). Therefore, we can immediately identify p = 1 and q = 2.Write parabola equation: Now that we have p and q, we can write the equation of the parabola as y = a(x – 1)(x – 2). However, we still need to find the value of the coefficient a. To do this, we will use the third point (3, –16) by substituting x with 3 and y with –16 in the equation and solving for a.Substitute third point: Substituting the point (3, –16) into the equation gives us –16 = a(3 – 1)(3 – 2). Simplifying the right side of the equation, we get –16 = a(2)(1), which simplifies further to –16 = 2a. Dividing both sides by 2, we find that a = –16 / 2 = –8.Solve for coefficient a: Having found a = –8, we can now write the complete equation of the parabola. Substituting a, p, and q into y = a(x – p)(x – q) gives us the final equation y = –8(x – 1)(x – 2).

Write the equation of the parabola that passes through the points $(1,0)$ , $(2,0)$ , and $(3,\text{–}16)$ . Write your answer in the form $y = a(x – p)(x – q)$ , where $a$ , $p$ , and $q$ are integers, decimals, or simplified fractions. $\newline$ ______

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