Question

Given the quadratic equation y=5x2+8x+9
𝑦
=
5
𝑥
2
+
8
𝑥
+
9
, solve for the y-coordinate of the parabola when x=−3
𝑥
=
−
3
.(1 point)
(−3
−
3
,)

Answer 1

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

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

Calculating each term:

1. \( (-3)^2 = 9 \)
2. \( 5(-3)^2 = 5 \times 9 = 45 \)
3. \( 8(-3) = -24 \)

Now, substituting these values back into the equation:

\[
y = 45 - 24 + 9
\]

Now, compute:

\[
y = 45 - 24 = 21
\]

\[
y = 21 + 9 = 30
\]

Thus, when \( x = -3 \), the y-coordinate of the parabola is \( y = 30 \).

Therefore, the point is:

\[
(-3, 30)
\]