The vertex of a parabola occurs where the derivative of its equation is 0, so an equation associated with the equation of a
parabola can be solved to find the x-coordinate of the vertex. Find the vertex of the parabola, given the equation of the
parabola and its associated equation.
-Equation of parabola: $f ( x ) = x ^ { 2 } - 6 x + 1$; associated equation: $0 = 2 x - 6$
A) $( 3 , - 8 )$
B) $( 3,28 )$
C) $( - 3,28 )$
D) $( - 3 , - 8 )$

Question

Quizplus · Accepted Answer

The associated equation $0 = 2x - 6$ is derived from taking the derivative of the parabola's equation $f(x) = x^2 - 6x + 1$ and setting it equal to zero to find the x-coordinate of the vertex. Solving $2x - 6 = 0$ gives $x = 3$. Substituting $x = 3$ into the original equation $f(x) = x^2 - 6x + 1$ gives $f(3) = 3^2 - 6*3 + 1 = 9 - 18 + 1 = -8$. Therefore, the vertex of the parabola is $(3, -8)$.

The Vertex of a Parabola Occurs Where the Derivative of Its