Çözüldü Parabola - Differentiation - Three-Variable Linear Equation System - Quadratic Equation

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https://collegeprep.uworld.com/sat/math-practice-tests-and-sample-questions/

Solution - 1:
(15 / 4 + x) / 2 = 2 ⇒ x = 1 / 4.

Solution - 2:
y = a·x^2 + b·x + c....(I)
0 = a·225 / 16 + b·15 / 4 + c....(II)
y' = 2a·x + b = 0 ⇒ x = -b / (2a)....(III) = 2 ⇒ b = -4a....(IV)
Substituting the value in (III) for its place in the equation (I), y = (4·a·c - 16·a^2) / (4·a) = 5 ⇒ c = 4a + 5....(V)
As homework for the interested students, solving the equation system formed by (II), (IV), and (V)
a = -80 / 49, b = 320 / 40, c = -75 / 49
y = -80·x^2 / 49 + 320·x / 40 - 75 / 49 = 0
-16·x^2 + 64·x - 15 = 0
x1 = 1 / 4, x2 = 15 / 4.