To analyze the function \( y = f(x) = x^2 + 8x - 5 \), we can follow these steps:

1. **Identify the type of function**: This is a quadratic function of the form \( ax^2 + bx + c \), where \( a = 1 \), \( b = 8 \), and \( c = -5 \).

2. **Find the vertex**: The vertex form of a quadratic is useful for determining its maximum or minimum. The vertex \( x \) coordinate can be found using \( x = -\frac{b}{2a} \):

\[
x = -\frac{8}{2 \cdot 1} = -4
\]

Substitute \( x = -4 \) back into the function to find the \( y \) coordinate of the vertex:

\[
y = (-4)^2 + 8(-4) - 5 = 16 - 32 - 5 = -21
\]

So the vertex is at \( (-4, -21) \).

3. **Determine the axis of symmetry**: The axis of symmetry is the line \( x = -4 \).

4. **Identify the direction**: Since \( a > 0 \), the parabola opens upward.

5. **Find the roots**: To find the roots, set \( f(x) = 0 \):

\[
x^2 + 8x - 5 = 0
\]

Use the quadratic formula:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{-8 \pm \sqrt{8^2 - 4 \cdot 1 \cdot (-5)}}{2 \cdot 1} = \frac{-8 \pm \sqrt{64 + 20}}{2} = \frac{-8 \pm \sqrt{84}}{2} = \frac{-8 \pm 2\sqrt{21}}{2}
\]

Thus, the roots are:

\[
x = -4 \pm \sqrt{21}
\]

6. **Conclusion**: The function \( y = x^2 + 8x - 5 \) has a vertex at \( (-4, -21) \), opens upward, and has two real roots given by \( x = -4 \pm \sqrt{21} \).

If you need to answer the specific questions listed (a, b, c, d), please provide the content of those options for further analysis.