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:

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