Question

Find the vertex of the parabola: y = x^2 - 57/10. Simplify both coordinates and write them as proper fractions, improper fractions, or integers.

Answer 1

To find the vertex of the parabola given by the equation \( y = x^2 - \frac{57}{10} \), we can use the standard form of a parabola, which is given by \( y = ax^2 + bx + c \).

In this particular case:
- \( a = 1 \)
- \( b = 0 \)
- \( c = -\frac{57}{10} \)

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

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

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

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

Now, we can find the y-coordinate of the vertex \( y_v \) by substituting the value of \( x_v \) back into the original equation:

\[
y_v = (0)^2 - \frac{57}{10} = 0 - \frac{57}{10} = -\frac{57}{10}
\]

Thus, the coordinates of the vertex are:

\[
\boxed{\left( 0, -\frac{57}{10} \right)}
\]