Question

Find the vertex of the parabola y = x^2.

Simplify both coordinates and write them as proper fractions, improper fractions, or integers.

Answer 1

The equation of the parabola is given by \( y = x^2 \).

To find the vertex of the parabola, we can observe that it is in the standard form \( y = ax^2 + bx + c \). In this case, we have:

- \( a = 1 \)
- \( b = 0 \)
- \( c = 0 \)

For a parabola described by this form, the x-coordinate of the vertex can be found using the formula:

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

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

\[
x = -\frac{0}{2 \cdot 1} = 0
\]

Now to find the y-coordinate of the vertex, substitute \( x = 0 \) back into the equation \( y = x^2 \):

\[
y = 0^2 = 0
\]

Therefore, the coordinates of the vertex are:

\[
(0, 0)
\]

In conclusion, the vertex of the parabola \( y = x^2 \) is at the point:

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