Question

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

x y
−3
54
−2
33
−1

0
1
2 9(1 point)
The high or low point of this parabola is (
,
).
Remaining Attempts : 3
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page 13 of 14

Answer 1

To complete the table of values for the quadratic equation \( y = 3x^2 - 6x + 9 \), we will substitute different \( x \) values into the equation.

We already have some values:
- For \( x = -3 \):
\[
y = 3(-3)^2 - 6(-3) + 9 = 3 \cdot 9 + 18 + 9 = 27 + 18 + 9 = 54
\]
- For \( x = -2 \):
\[
y = 3(-2)^2 - 6(-2) + 9 = 3 \cdot 4 + 12 + 9 = 12 + 12 + 9 = 33
\]
- For \( x = -1 \):
\[
y = 3(-1)^2 - 6(-1) + 9 = 3 \cdot 1 + 6 + 9 = 3 + 6 + 9 = 18
\]
- For \( x = 0 \):
\[
y = 3(0)^2 - 6(0) + 9 = 0 - 0 + 9 = 9
\]
- For \( x = 1 \):
\[
y = 3(1)^2 - 6(1) + 9 = 3 \cdot 1 - 6 + 9 = 3 - 6 + 9 = 6
\]
- For \( x = 2 \):
\[
y = 3(2)^2 - 6(2) + 9 = 3 \cdot 4 - 12 + 9 = 12 - 12 + 9 = 9
\]

Now, we can complete the table with the calculated values:
```
x | y
-----------
−3 | 54
−2 | 33
−1 | 18
0 | 9
1 | 6
2 | 9
```
To find the high or low point of the parabola, we recognize that the vertex of a parabola in the form \( y = ax^2 + bx + c \) can be found using the formula for the x-coordinate of the vertex, given by \( x = -\frac{b}{2a} \).

Here, \( a = 3 \) and \( b = -6 \):
\[
x = -\frac{-6}{2 \cdot 3} = \frac{6}{6} = 1
\]

Now we substitute \( x = 1 \) back into the equation to find the y-coordinate of the vertex:
\[
y = 3(1)^2 - 6(1) + 9 = 3 - 6 + 9 = 6
\]

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

**Final Answer: The high or low point of this parabola is (1, 6).**