Question

what is the vertex of the function $f(x)=x^2 + 12x$? $(6, 0)$ $(-6, 0)$ $(6, -36)$ $(-6, -36)$

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 \( x = -\frac{b}{2a} \). In the function \( f(x)=x^{2}+12x \), we have \( a = 1 \) and \( b = 12 \).

Step2: Calculate x - coordinate of vertex

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

Step3: Calculate y - coordinate of vertex

Substitute \( x=-6 \) into the function \( f(x)=x^{2}+12x \). Then \( f(-6)=(-6)^{2}+12\times(-6)=36 - 72=-36 \).

Answer:

\((-6, - 36)\)