1. Homework Statement

1a) Solve f(x) = x^2- 4x+m in the form f(x) = (x-a)^2+ b
1b) What is the smallest value f(x) can have?

3. The Attempt at a Solution

1a) Seems simple enough. I set f(x) to 0 and used the completing the square method to solve. Ended up with f(x)=(x-2)^2+ m-4.

I don’t know how to approach 1b) though. I’m assuming I’ve made a mistake somewhere – there is no smallest value f(x) can have without knowing the value of m. Is there a way to find m that I haven't picked up on, or would the answer just be m - 4?

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1. Homework Statement

1a) Solve f(x) = x^2- 4x+m in the form f(x) = (x-a)^2+ b
1b) What is the smallest value f(x) can have?

3. The Attempt at a Solution

1a) Seems simple enough. I set f(x) to 0 and used the completing the square method to solve. Ended up with f(x)=(x-2)^2+ m-4.

I don’t know how to approach 1b) though. I’m assuming I’ve made a mistake somewhere – there is no smallest value f(x) can have without knowing the value of m. Is there a way to find m that I haven't picked up on, or would the answer just be m - 4?

Looks fine to me.

HallsofIvy
Homework Helper
1. Homework Statement

1a) Solve f(x) = x^2- 4x+m in the form f(x) = (x-a)^2+ b
1b) What is the smallest value f(x) can have?

3. The Attempt at a Solution

1a) Seems simple enough. I set f(x) to 0 and used the completing the square method to solve. Ended up with f(x)=(x-2)^2+ m-4.

I don’t know how to approach 1b) though. I’m assuming I’ve made a mistake somewhere – there is no smallest value f(x) can have without knowing the value of m. Is there a way to find m that I haven't picked up on, or would the answer just be m - 4?