Question

what are the coordinates of the vertex of the function f(x) = x² - 12x + 5?
○ (6, 31)
○ (-6, 31)
○ (6, -31)
○ (-6, -31)

Explanation:

Step1: Recall vertex formula for parabola

For a quadratic function \( f(x) = ax^2 + bx + c \), the x - coordinate of the vertex is given by \( x=-\frac{b}{2a} \). Here, \( a = 1 \), \( b=- 12 \), \( c = 5 \).

Step2: Calculate x - coordinate

Substitute \( a = 1 \) and \( b=-12 \) into the formula: \( x=-\frac{-12}{2\times1}=\frac{12}{2} = 6 \).

Step3: Calculate y - coordinate

Substitute \( x = 6 \) into the function \( f(x)=x^{2}-12x + 5 \). So \( f(6)=6^{2}-12\times6 + 5=36-72 + 5=36 + 5-72=41 - 72=-31 \).

Answer:

(6, -31)