Question

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=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 \(y = 2x^2 + (-20)x + 40\)**.