Question

Convert the quadratic y = 2(x-5)^2-10 from vertex form to standard form. (2 points) + The standard form of the quadratic is y

Answer 1

To convert the quadratic from vertex form to standard form, we start with the vertex form of the equation:

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

Next, we will expand the squared term and then simplify the equation.

1. Expand \((x - 5)^2\):
\[
(x - 5)^2 = x^2 - 10x + 25
\]

2. Substitute this back into the equation:
\[
y = 2(x^2 - 10x + 25) - 10
\]

3. Distribute the 2:
\[
y = 2x^2 - 20x + 50 - 10
\]

4. Combine like terms:
\[
y = 2x^2 - 20x + 40
\]

Now the quadratic in standard form is:

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