Question

Given this table of values, complete the table for the quadratic equation y=3x2−6x+9
𝑦
=
3
𝑥
2
−
6
𝑥
+
9
to find the values of the high or low point of the parabola.

x y
−3
−
3
54
−2
−
2
33
−1
−
1

0
1
2 9
(1 point)
The high or low point of this parabola is (,).

Answer 1

To find the vertex (high or low point) of the parabola defined by 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 can be found using the formula:

\[
x = -\frac{b}{2a}
\]

In this case, we have:

- \( a = 3 \)
- \( b = -6 \)
- \( c = 9 \)

Plugging in the values into the formula:

\[
x = -\frac{-6}{2 \cdot 3} = \frac{6}{6} = 1
\]

Now, we can find the y-coordinate of the vertex by substituting \( x = 1 \) back into the original equation:

\[
y = 3(1)^2 - 6(1) + 9
\]
\[
y = 3(1) - 6 + 9 = 3 - 6 + 9 = 6
\]

Thus, the vertex (high or low point) of the parabola is at the point \( (1, 6) \).

So, the high or low point of this parabola is \((1, 6)\).