Convert the quadratic y = 2(x−5)2 − 10

Question

from vertex form to standard form.(2 points)
The standard form of the quadratic is y=
x2+

Answer 1

To convert the quadratic \( y = 2(x - 5)^2 - 10 \) from vertex form to standard form, we will first expand the equation.

1. Start with the vertex form: \[ y = 2(x - 5)^2 - 10 \]

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

So the standard form of the quadratic is: \[ y = 2x^2 - 20x + 40 \]

Thus, filling in the required format, we have: \[ y = x^2 + (-20) + 40, \] where the coefficient of \(x^2\) is \(2\).

So if you want the final answer as: \[ y = 2x^2 - 20x + 40 \]