Question

Select all of the zeroes of the function f(x)=x²−4x+4.

a) x=2
b) x=4
c) x=−2
d)x=0

Answer 1

The zero of the quadratic function f(x) = x² - 4x + 4 is x = 2, which is a double root. This is found by factoring the equation, resulting in (x - 2)² = 0.

Step-by-step explanation:

The student is asking to find all the zeroes of the quadratic function f(x) = x² - 4x + 4. To solve for the roots of a quadratic equation of the form ax² + bx + c = 0, we can factor, complete the square, or use the quadratic formula.

In this case, the equation f(x) = x² - 4x + 4 factors into (x - 2)² = 0, suggesting that the sole zero of the function is x = 2. Since this is a perfect square trinomial, it has one unique solution where the graph of the function touches the x-axis at one point, also referred to as a double root.

The answer choices provided were a) x=2, b) x=4, c) x=−2, and d)x=0. From our calculation, we only select a) x=2 as the zero of the function.