Identify the vertex of the parabola.
-$$y = x ^ { 2 } - 12 x + 37$$
A) $( 0,6 )$
B) $( 6,1 )$
C) $( 1,6 )$
D) $( 1,0 )$

Question

Quizplus · Accepted Answer

The vertex of a parabola in the form $y = ax^2 + bx + c$ can be found using the formula $(- \frac{b}{2a}, f(- \frac{b}{2a}))$. For the given equation $y = x^2 - 12x + 37$, $a = 1$, $b = -12$, and $c = 37$. Thus, the x-coordinate of the vertex is $- \frac{-12}{2*1} = 6$. Plugging this back into the equation gives the y-coordinate: $y = (6)^2 - 12(6) + 37 = 36 - 72 + 37 = 1$. Therefore, the vertex is $(6, 1)$.

Identify the Vertex of the Parabola y=x2−12x+37y = x ^ { 2 } - 12 x + 37y=x2−12x+37

Identify the Vertex of the Parabola $y = x ^ { 2 } - 12 x + 37$