Question

What is the x-coordinate of the vertex of the parabola given by the function f(x) = x^2 + 5x - 3?

Answer 1

To find the x-coordinate of the vertex of a parabola given by a quadratic function in the form of \( f(x) = ax^2 + bx + c \), we can use the formula:

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

In the function \( f(x) = x^2 + 5x - 3 \), the coefficients are:
- \( a = 1 \)
- \( b = 5 \)
- \( c = -3 \)

Now we can substitute the values of \( a \) and \( b \) into the formula:

\[
x = -\frac{5}{2 \cdot 1} = -\frac{5}{2}
\]

Thus, the x-coordinate of the vertex of the parabola is

\[
\boxed{-\frac{5}{2}}.
\]