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+
.
Remaining Attempts : 3

Answer 1

To convert the quadratic equation from vertex form to standard form, we start with the given vertex form:

\[ y = 2(x - 5)^2 - 10 \]

### Step 1: Expand the vertex form
First, we need to expand \((x - 5)^2\):

\[
(x - 5)^2 = x^2 - 10x + 25
\]

### Step 2: Substitute back into the equation
Now, substitute this expansion back into the original equation:

\[
y = 2(x^2 - 10x + 25) - 10
\]

### Step 3: Distribute the 2
Next, distribute the 2:

\[
y = 2x^2 - 20x + 50 - 10
\]

### Step 4: Combine like terms
Now, combine the constants:

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

### Result
Now we can write the standard form of the quadratic, which is:

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

Thus, we have:

- The standard form is \(y = 2x^2 + (-20)x + 40\).

So the answer is:
- \(y = 2x^2 - 20x + 40\).