To find the y-coordinate of the parabola described by the equation \( y = 5x^2 + 8x + 9 \) when \( x = -3 \), we can substitute \( -3 \) for \( x \) in the equation.
Starting with the equation:
\[ y = 5x^2 + 8x + 9 \]
Substituting \( x = -3 \):
\[ y = 5(-3)^2 + 8(-3) + 9 \]
Now, calculating each term step-by-step:
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Calculate \( (-3)^2 \): \[ (-3)^2 = 9 \]
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Multiply by 5: \[ 5 \cdot 9 = 45 \]
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Calculate \( 8(-3) \): \[ 8 \cdot (-3) = -24 \]
Now substituting these back into the equation for \( y \):
\[ y = 45 - 24 + 9 \]
Calculating it step-by-step:
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First combine \( 45 - 24 \): \[ 45 - 24 = 21 \]
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Now add \( 9 \): \[ 21 + 9 = 30 \]
Thus, the y-coordinate when \( x = -3 \) is:
\[ y = 30 \]
So the point on the parabola is:
\[ (-3, 30) \]