How do you rewrite the quadratic function fx = 2(x – 2)^2 + 32 into standard form?

Converting Vertex Form to Standard Form

To convert the given vertex form of the function f(x) = 2(x - 2)^2 + 32 into standard form, we’ll follow a systematic approach.

Step 1: Expand the Squared Term

Start by expanding the squared term:

(x - 2)^2 = x^2 - 4x + 4

Now substitute this back into the original function:

f(x) = 2(x^2 - 4x + 4) + 32

Step 2: Distribute the Coefficient

Next, distribute the coefficient (2) to each term inside the parentheses:

f(x) = 2x^2 - 8x + 8 + 32

Step 3: Combine Constant Terms

Now, combine the constant terms (8 and 32):

f(x) = 2x^2 - 8x + 40

Conclusion

The standard form of the quadratic function is:

f(x) = 2x^2 - 8x + 40

This is how you rewrite a function from vertex form to standard form!