Question

Find the y-coordinate of the parabola y = 5x^2 + 8x + 9.
The x-coordinate is -3.
(-3,?)

Answer 1

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

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

First, calculate \((-3)^2\):

\[
(-3)^2 = 9
\]

Now substitute this value into the equation:

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

Next, calculate \(5(9)\):

\[
5(9) = 45
\]

Now calculate \(8(-3)\):

\[
8(-3) = -24
\]

Now substitute these values into the equation:

\[
y = 45 - 24 + 9
\]

Combine the terms:

\[
y = 45 - 24 = 21
\]
\[
y = 21 + 9 = 30
\]

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

So, the point is \((-3, 30)\).