Question

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

Answer 1

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:

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

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

3. 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:

1. First combine \( 45 - 24 \):
\[
45 - 24 = 21
\]

2. Now add \( 9 \):
\[
21 + 9 = 30
\]

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

\[
y = 30
\]

So the point on the parabola is:

\[
(-3, 30)
\]