Given the quadratic equation y=5x2+8x+9 , solve for the y-coordinate of the parabola when x=−3

1 answer

To find the y-coordinate of the parabola given the quadratic equation \( y = 5x^2 + 8x + 9 \) when \( x = -3 \), we substitute \( x = -3 \) into the equation.

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

Now calculate each term:

  1. \( (-3)^2 = 9 \)
  2. \( 5 \times 9 = 45 \)
  3. \( 8 \times (-3) = -24 \)

Now substitute these values back into the equation:

\[ y = 45 - 24 + 9 \]

Now compute the sum:

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

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

\[ \boxed{30} \]