To find the high or low point (the vertex) of the quadratic equation \( y = 3x^2 - 6x + 9 \), we can use the vertex formula. For a quadratic equation in the standard form \( y = ax^2 + bx + c \), the x-coordinate of the vertex is given by the formula:
\[ x = -\frac{b}{2a} \]
In your equation, \( a = 3 \) and \( b = -6 \).
Let's calculate the x-coordinate of the vertex:
\[ x = -\frac{-6}{2 \cdot 3} = \frac{6}{6} = 1 \]
Next, we can find the y-coordinate by substituting \( x = 1 \) back into the original equation:
\[ y = 3(1)^2 - 6(1) + 9 \] \[ y = 3(1) - 6 + 9 \] \[ y = 3 - 6 + 9 \] \[ y = 6 \]
Thus, the coordinates of the vertex, which gives us the low point of the parabola, are \( (1, 6) \).
To complete the given table of values, you may need specific x-values to calculate corresponding y-values. If the table is not provided, please share the specific x-values you wish to evaluate, and I can help calculate the corresponding y-values using the equation \( y = 3x^2 - 6x + 9 \).