Question: The function f(x) = x^2 - 4x + 4 can be expressed in which form?
Options:
(x - 2)^2
(x + 2)^2
(x - 4)^2
(x + 4)^2
Correct Answer: (x - 2)^2
Solution:
f(x) = (x - 2)^2 is the completed square form.
The function f(x) = x^2 - 4x + 4 can be expressed in which form?
Practice Questions
Q1
The function f(x) = x^2 - 4x + 4 can be expressed in which form?
(x - 2)^2
(x + 2)^2
(x - 4)^2
(x + 4)^2
Questions & Step-by-Step Solutions
The function f(x) = x^2 - 4x + 4 can be expressed in which form?
Correct Answer: (x - 2)^2
Step 1: Start with the function f(x) = x^2 - 4x + 4.
Step 2: Identify the coefficients in the quadratic expression. Here, the coefficient of x^2 is 1, the coefficient of x is -4, and the constant term is 4.
Step 3: To complete the square, take the coefficient of x (-4), divide it by 2 to get -2, and then square it to get 4.
Step 4: Rewrite the function by grouping the first two terms: f(x) = (x^2 - 4x) + 4.
Step 5: Replace (x^2 - 4x) with the completed square form: f(x) = (x - 2)^2.
Step 6: Add the constant term back: f(x) = (x - 2)^2.
Quadratic Functions – Understanding the standard form of quadratic functions and how to complete the square.
Completing the Square – The process of rewriting a quadratic function in the form (x - h)^2 + k.
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