Question

Which form do you prefer when finding the vertex of a quadratic function, vertex or standard? Why?

Answer 1

While the standard quadratic form is a x 2 + b x + c = y , the vertex form of a quadratic equation is y = a ( x − h ) 2 + k .

Answer 2

I prefer using vertex form when finding the vertex of a quadratic function. This is because it directly reveals the vertex coordinates without any further calculations.

Step-by-step explanation:

Vertex form: f(x) = a(x - h)^2 + k, where (h, k) is the vertex.

Standard form: f(x) = ax^2 + bx + c.

Finding the vertex in standard form requires:

Completing the square, which can be tedious and algebraically messy.

Identifying the vertex as the midpoint of the roots, which involves additional calculations.

In contrast, vertex form directly presents the vertex coordinates (h, k), eliminating the need for additional steps. This makes it a more efficient and straightforward approach to finding the vertex.

However, if your goal is to analyze the parabola's behavior (e.g., direction of opening), standard form might be more convenient due to its explicit coefficients. Ultimately, the preferred form depends on the specific task at hand.