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