Question

A quadratic function f is given. f(x) = x² +4x +3
(a) Express f in standard form.

Answer 1

To express the quadratic function f(x) = x² +4x +3 in standard form, we complete the square to get f(x) = (x + 2)² - 1. Completing the square involves transforming the quadratic function into the form f(x) = (x + h)² + k. In this case, f(x) = (x + 2)² - 1, achieving standard form.

Step-by-step explanation:

The student asks to express a quadratic function in standard form. The given function is f(x) = x² +4x +3. To express this equation in standard form, which is f(x) = a(x - h)² + k, we need to complete the square.

1. First, factor out the leading coefficient, which in this case is 1 (since it's just x² this step isn't needed).
2. Next, take half of the x-coefficient (4/2 = 2), square it (2² = 4), and add and subtract this number inside the parentheses.
3. This gives us f(x) = (x + 2)² - 4 + 3, which simplifies to f(x) = (x + 2)² - 1.

The standard form of the given quadratic function is f(x) = (x + 2)² - 1.