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

Question

from vertex form to standard form
The standard form of the quadratic is y=_x2+_x+_.

Answer 1

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

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

So the coefficients are:

• The coefficient of \( x^2 \) is \( 2 \).
• The coefficient of \( x \) is \( -20 \).
• The constant term is \( 40 \).

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