Question

y=3(x-4)^2+2 in standard form

Answer 1

To convert the equation \( y = 3(x - 4)^2 + 2 \) into standard form, we need to expand it.

1. Start with the given equation:
\[
y = 3(x - 4)^2 + 2
\]

2. Expand the squared term:
\[
(x - 4)^2 = x^2 - 8x + 16
\]

3. Substitute this back into the equation:
\[
y = 3(x^2 - 8x + 16) + 2
\]

4. Distribute the \( 3 \):
\[
y = 3x^2 - 24x + 48 + 2
\]

5. Combine like terms:
\[
y = 3x^2 - 24x + 50
\]

Now, the equation is in standard form, which is typically expressed as:
\[
y = ax^2 + bx + c
\]

Thus, the standard form of the equation is:
\[
y = 3x^2 - 24x + 50
\]