Question

Given this table of values, complete the table for the quadratic equation y = 3x^2 - 6x + 9 to find the values of the high or low point of the parabola.

Answer 1

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 \( y = 3x^2 - 6x + 9 \).