Graphs of Quadratic Equations Practice

Question

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Question
Given the quadratic equation y=5x2+8x+9
, solve for the y-coordinate of the parabola when x=−3
.(1 point)
(−3
,
)
Remaining Attempts : 3

Answer 1

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

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

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

3. Substitute this 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. Now, put everything back into the equation: \[ y = 45 - 24 + 9 \]

7. Combine the numbers: \[ 45 - 24 = 21 \] \[ 21 + 9 = 30 \]

So, the y-coordinate when \( x = -3 \) is \( 30 \).

The final answer is: \[ (-3, 30) \]