Question

Build the equation that combines the functions t=x−3 and y = 4t2 . Show your work. You can use math type or insert a picture of your work.

Answer 1

To combine the functions \( t = x - 3 \) and \( y = 4t^2 \), we can substitute the expression for \( t \) into the equation for \( y \).

1. Start with the function for \( t \):
\[
t = x - 3
\]

2. Now substitute \( t \) into the function for \( y \):
\[
y = 4t^2
\]

Replacing \( t \) with \( x - 3 \):
\[
y = 4(x - 3)^2
\]

3. Now let's expand \( (x - 3)^2 \):
\[
(x - 3)^2 = x^2 - 6x + 9
\]

4. Substituting this back in gives:
\[
y = 4(x^2 - 6x + 9)
\]

5. Distributing \( 4 \) across the terms within the parentheses:
\[
y = 4x^2 - 24x + 36
\]

So the final equation that combines the functions \( t \) and \( y \) is:
\[
y = 4x^2 - 24x + 36
\]