Question

find the coordinates of the vertex for the parabola defined by the given quadratic function.

$f(x) = 3x^2 - 12x + 4$

the vertex is \\(\square\\). (type an ordered pair.)

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, \( a = 3 \), \( b=- 12 \), so \( x=-\frac{-12}{2\times3}=\frac{12}{6} = 2 \).

Step2: Find y - coordinate of vertex

Substitute \( x = 2 \) into the function \( f(x)=3x^{2}-12x + 4 \).
\( f(2)=3\times(2)^{2}-12\times(2)+4=3\times4-24 + 4=12-24 + 4=-8 \).

Answer:

\((2,-8)\)