Given the quadratic equation y = 5x^2 + 8x + 9 , solve for the y-coordinate of the parabola when x = -3

1 answer

To find the y-coordinate of the parabola described by the equation \( y = 5x^2 + 8x + 9 \) when \( x = -3 \), we can substitute \( -3 \) into the equation for \( x \):

\[ y = 5(-3)^2 + 8(-3) + 9 \]

Calculating each term step by step:

  1. Calculate \( (-3)^2 \):

\[ (-3)^2 = 9 \]

  1. Multiply by 5:

\[ 5 \times 9 = 45 \]

  1. Calculate \( 8(-3) \):

\[ 8 \times -3 = -24 \]

  1. Now substitute these values back into the equation:

\[ y = 45 - 24 + 9 \]

  1. Combine the terms:

\[ 45 - 24 = 21 \] \[ 21 + 9 = 30 \]

Thus, the y-coordinate of the parabola when \( x = -3 \) is:

\[ \boxed{30} \]