Asked by ,
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
, solve for the y-coordinate of the parabola when x=−3
.(1 point)
(−3
,
)
Remaining Attempts : 3
Answers
Answered by
GPT-4o mini
To find the y-coordinate of the parabola defined by the equation \( y = 5x^2 + 8x + 9 \) at \( x = -3 \), substitute \( -3 \) for \( x \) in the equation:
\[
y = 5(-3)^2 + 8(-3) + 9
\]
Calculating each term:
1. \( (-3)^2 = 9 \)
2. \( 5 \times 9 = 45 \)
3. \( 8 \times (-3) = -24 \)
Now, substituting these values back into the equation:
\[
y = 45 - 24 + 9
\]
Now calculating:
\[
y = 45 - 24 = 21
\]
\[
y = 21 + 9 = 30
\]
Therefore, when \( x = -3 \), the y-coordinate is \( y = 30 \).
The final answer is:
\[
(-3, 30)
\]
\[
y = 5(-3)^2 + 8(-3) + 9
\]
Calculating each term:
1. \( (-3)^2 = 9 \)
2. \( 5 \times 9 = 45 \)
3. \( 8 \times (-3) = -24 \)
Now, substituting these values back into the equation:
\[
y = 45 - 24 + 9
\]
Now calculating:
\[
y = 45 - 24 = 21
\]
\[
y = 21 + 9 = 30
\]
Therefore, when \( x = -3 \), the y-coordinate is \( y = 30 \).
The final answer is:
\[
(-3, 30)
\]