Question

Findthevertexoftheparabolay = x2.


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

Answer 1

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

This is a standard form of a parabola that opens upwards. The vertex of a parabola defined by the equation \( y = ax^2 + bx + c \) can be found using the formula for the x-coordinate of the vertex, which is given by:

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

In the case of the equation \( y = x^2 \):

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

Plugging in the values for \( a \) and \( b \):

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

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

\[
y = 0^2 = 0
\]

Thus, the vertex of the parabola \( y = x^2 \) is at the point \( (0, 0) \).

In summary, the vertex is:

\[
\text{Vertex} = (0, 0)
\]