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+ ? x+ ? .

Answer 1

To convert the quadratic from vertex form \( y = 2(x - 5)^2 - 10 \) to standard form, we need to 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: \[ y = 2x^2 - 20x + 40 \]

Now we have it in the standard form \( y = ax^2 + bx + c \), where \( a = 2 \), \( b = -20 \), and \( c = 40 \).

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

So the completed equation is: The standard form of the quadratic is \(y = 2x^2 + (-20)x + 40\).