Question

question 7 · 1 point
determine the vertex of the graph of the following parabola.
$f(x)=3x^{2}-6x + 1$
give your answer as an ordered pair $(h,k)$.
provide your answer below:

Explanation:

Step1: Identify coefficients

For the quadratic function $f(x)=ax^{2}+bx + c$, here $a = 3$, $b=-6$, $c = 1$.

Step2: Calculate x - coordinate of vertex

The formula for the x - coordinate $h$ of the vertex of a parabola is $h=-\frac{b}{2a}$. Substitute $a = 3$ and $b=-6$ into the formula: $h=-\frac{-6}{2\times3}=\frac{6}{6}=1$.

Step3: Calculate y - coordinate of vertex

Substitute $x = h = 1$ into the function $f(x)=3x^{2}-6x + 1$. Then $f(1)=3\times1^{2}-6\times1 + 1=3-6 + 1=-2$.

Answer:

$(1,-2)$