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: \[ y = 4x^2 - 24x + 36 \]