Which of the following equations has a maximum at (9,7)A. y = -12 + 141 - 40B. y = -12 -180 -88c. y = -12 + 18a - 74D.y = –12 – 14. – 58
Accepted Solution
A:
Answer:Step-by-step explanation:Answer:option C ⇒ C) y = -x² + 18x - 74Step-by-step explanation:The given options are:A) y = -x² + 14x - 40B) y = -x² - 18x - 88C) y = -x² + 18x - 74D) y = -x² - 14x - 58=================================The general equation of the parabola has the form:y = f(x) = ax² + bx + cThe vertex of the parabola has the coordinates (h , k)where h = [tex]\frac{-b}{2a}[/tex]and k = f(h) = f([tex]\frac{-b}{2a}[/tex])Check option A: a = -1 , b = 14 ⇒ (h,k) = (7, f(7) ) = (7 , 9)Check option B: a = -1 , b = -18 ⇒ (h,k) = (-9, f(-9) ) = (-9,-7)Check option C: a = -1 , b = 18 ⇒ (h,k) = (9, f(9) ) = (9,7)Check option D: a = -1 , b = -14 ⇒ (h,k) = (-7, f(7) ) = (-7,-9)So the equation which has a maximum at (9,7) ⇒ y = -x² + 18x - 74So, the correct answer is option C