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 \( y = 2(x - 5)^2 - 10 \) from vertex form 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 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 the standard form of the quadratic: \[ y = 2x^2 - 20x + 40 \]

So, the standard form is: \[ y = 2x^2 + (-20)x + 40 \]

Thus, in the format requested, the answer is:

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