To find the y-coordinate of the parabola defined by the quadratic equation \( y = 5x^2 + 8x + 9 \) when \( x = -3 \), substitute \( -3 \) for \( x \) in the equation.
\[ y = 5(-3)^2 + 8(-3) + 9 \]
Calculating each term step by step:
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Calculate \( (-3)^2 \): \[ (-3)^2 = 9 \]
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Multiply by 5: \[ 5 \times 9 = 45 \]
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Calculate \( 8(-3) \): \[ 8 \times -3 = -24 \]
Now substitute these values back into the equation: \[ y = 45 - 24 + 9 \]
Combine the values: \[ y = 45 - 24 = 21 \] \[ y = 21 + 9 = 30 \]
Therefore, the y-coordinate when \( x = -3 \) is \( y = 30 \).
Thus, the coordinates are \( (-3, 30) \).
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