Question

Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an left parenthesis, x, comma, y, right parenthesis(x,y) point.
y, equals, minus, x, squared, plus, 6
y=−x
2
+6

Answer 1

To find the coordinates of the vertex of the parabola given by the equation \( y = -x^2 + 6 \), we can use the vertex formula for a parabola in the standard form \( y = ax^2 + bx + c \).

In this case:
- \( a = -1 \)
- \( b = 0 \)
- \( c = 6 \)

The x-coordinate of the vertex \( x_v \) can be found using the formula:

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

Substituting the values of \( a \) and \( b \):

\[
x_v = -\frac{0}{2(-1)} = 0
\]

Now, we substitute \( x_v = 0 \) back into the original equation to find the y-coordinate of the vertex \( y_v \):

\[
y_v = - (0)^2 + 6 = 6
\]

Thus, the coordinates of the vertex are:

\[
\boxed{(0, 6)}
\]