Given the quadratic equation y=5x2+8x+9

, solve for the y-coordinate of the parabola when x=−3
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1 answer

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

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

Now, calculate each term step by step:

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

  2. Multiply by 5: \[ 5 \cdot 9 = 45 \]

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

  4. Now, combine all the results: \[ y = 45 - 24 + 9 \]

  5. Simplify: \[ 45 - 24 = 21 \] \[ 21 + 9 = 30 \]

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

\[ \boxed{30} \]