To find the y-coordinate of the parabola defined by the equation \( y = 5x^2 + 8x + 9 \) at \( x = -3 \), substitute \( -3 \) for \( x \) in the equation:
\[ y = 5(-3)^2 + 8(-3) + 9 \]
Calculating each term:
- \( (-3)^2 = 9 \)
- \( 5 \times 9 = 45 \)
- \( 8 \times (-3) = -24 \)
Now, substituting these values back into the equation:
\[ y = 45 - 24 + 9 \]
Now calculating:
\[ y = 45 - 24 = 21 \] \[ y = 21 + 9 = 30 \]
Therefore, when \( x = -3 \), the y-coordinate is \( y = 30 \).
The final answer is:
\[ (-3, 30) \]