Question

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

Answer 1

The quadratic function f(x) = x²+4x+3 in standard form is f(x) = (x + 2)² - 1. This is achieved by completing the square which involves adding and subtracting the square of half the coefficient of the x term.

Step-by-step explanation:

To express the quadratic function f(x) = x²+4x+3 in standard form, we need to complete the square. The standard form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Here are the steps we follow to complete the square:

1. Start with the original equation: f(x) = x² + 4x + 3.
2. Factor out the coefficient of the x² term if it is not 1. In this case, it is already 1, so we can skip this step.
3. Divide the coefficient of the x term by 2 and square the result to find the number that completes the square. Here, 4/2 = 2 and 2² = 4.
4. Add and subtract this number within the parentheses: f(x) = (x² + 4x + 4) - 4 + 3.
5. Rewrite the quadratic portion as a squared binomial: f(x) = (x + 2)² - 1. This is the standard form.

Standard form: f(x) = (x + 2)² - 1