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

  1. Substitute \( x = -3 \): \[ y = 5(-3)^2 + 8(-3) + 9 \]

  2. Calculate \( (-3)^2 \): \[ (-3)^2 = 9 \]

  3. Substitute back into the equation: \[ y = 5(9) + 8(-3) + 9 \]

  4. Calculate \( 5(9) \): \[ 5(9) = 45 \]

  5. Calculate \( 8(-3) \): \[ 8(-3) = -24 \]

  6. Substitute these values into the equation: \[ y = 45 - 24 + 9 \]

  7. Now simplify: \[ y = 21 + 9 = 30 \]

Therefore, the y-coordinate of the parabola when \( x = -3 \) is \( \boxed{30} \).