flâneur

MyPractice - SAT Practice 4 - February 25, 2024 - Details

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In the xy-plane, a parabola has vertex  ( 9 , - 14 ) and intersects the 𝑥 -axis at two points. If the equation of the parabola is written in the form 𝑦 = 𝑎 𝑥 2 + 𝑏 𝑥 + 𝑐 , where 𝑎 , 𝑏 , and 𝑐 are constants, which of the following could be the value of 𝑎 + 𝑏 + 𝑐 ? - 23 - 19 - 14 - 12 Choice D is correct. The equation of a parabola in the xy-plane can be written in the form 𝑦 = 𝑎 𝑥 - ℎ 2 + 𝑘 , where 𝑎 is a constant and  ℎ , 𝑘 is the vertex of the parabola. If 𝑎 is positive, the parabola will open upward, and if 𝑎 is negative, the parabola will open downward. It’s given that the parabola has vertex 9 , - 14 . Substituting 9 for ℎ and - 14 for 𝑘 in the equation  𝑦 = 𝑎 𝑥 - ℎ 2 + 𝑘 gives 𝑦 = 𝑎 𝑥 - 9 2 - 14 , which can be rewritten as 𝑦 = 𝑎 𝑥 - 9 𝑥 - 9 - 14 , or 𝑦 = 𝑎 𝑥 2 - 18 𝑥 + 81 - 14 . Distributing the factor of 𝑎 on the right-hand side of this equation yields 𝑦 = 𝑎 𝑥 2 - 18 𝑎 𝑥 + 81 𝑎 - 14 . Therefore, the equat

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