Question

y= 2(x-5)^2 -10
Write in standard form

Answer 1

To write the given equation \( y = 2(x - 5)^2 - 10 \) in standard form, we will first expand the quadratic expression.

1. Start with the equation:

\[
y = 2(x - 5)^2 - 10
\]

2. Expand \( (x - 5)^2 \):

\[
(x - 5)^2 = x^2 - 10x + 25
\]

3. Substitute this back into the equation:

\[
y = 2(x^2 - 10x + 25) - 10
\]

4. Distribute the \( 2 \):

\[
y = 2x^2 - 20x + 50 - 10
\]

5. Combine like terms:

\[
y = 2x^2 - 20x + 40
\]

Now, the equation is in standard form, which is generally represented as:

\[
y = ax^2 + bx + c
\]

Thus, the standard form of the given equation is:

\[
y = 2x^2 - 20x + 40
\]