Question

Given the quadratic equation y=5x2+8x+9
, solve for the y-coordinate of the parabola when x=−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 \( x \) with \(-3\) in the equation:

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

Now, calculate each term step by step:

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

2. Multiply by 5:
\[
5 \cdot 9 = 45
\]

3. Calculate \( 8(-3) \):
\[
8 \cdot (-3) = -24
\]

4. Now, combine all the results:
\[
y = 45 - 24 + 9
\]

5. Simplify:
\[
45 - 24 = 21
\]
\[
21 + 9 = 30
\]

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

\[
\boxed{30}
\]