Question

A graph of quadratic function y = f(x) is shown below.
What is the solution set of the quadratic inequality f(x) ≥ 0?

Answer 1

Answer:

{f|0 ≤ f(x)}; x² - 4x + 5

Step-by-step explanation:

To find the Quadratic Equation, plug the vertex into the Vertex Equation FIRST, y = a(x - h)² + k, where (h, k) → (2, 1) is the vertex, plus, -h gives you the OPPOSITE terms of what they really are, and k gives you the EXACT terms of what they really are: (x - 2)² + 1. Doing this will give you the Quadratic Equation of x² - 4x + 5. You understand now?

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Answer 2

The solution set of the quadratic inequality f(x) ≥ 0 is the set of all Real numbers as per the general equation of a parabola.

What is the general equation of a parabola?

The general equation of a parabola in vertex form is

y = a(x - h)² + k

Where, the coordinate (h, k) represents the vertex of the parabola.

Here, the given function represents a parabola.

Therefore the equation of the parabola  is, y = f(x) = a(x - h)² + k

Where, (h, k) is the coordinate (2, 1).

As the given function is a parabolic function, therefore, the required inequality f(x) ≥ 0 is true for all the values.

Therefore, the set of all Real numbers satisfies f(x) ≥ 0.

Learn more about the parabola here: https://brainly.com/question/10442288

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