Question

1. find the vertex of the parabola.

y = 3x² - 6x + 7
○ (1,4)
○ (3,7)
○ (-6,7)
○ (3,-6)

Explanation:

Step1: Recall vertex formula for parabola

For a parabola in the form \( y = ax^2 + bx + c \), the x - coordinate of the vertex is given by \( x=-\frac{b}{2a} \). In the equation \( y = 3x^2-6x + 7 \), we have \( a = 3 \) and \( b=-6 \).
So, \( x =-\frac{-6}{2\times3}=\frac{6}{6} = 1 \).

Step2: Find the y - coordinate of the vertex

Substitute \( x = 1 \) into the equation \( y=3x^2-6x + 7 \).
\( y=3\times(1)^2-6\times(1)+7=3 - 6 + 7=4 \).

Answer:

\((1,4)\)