Question

Choose the correct answer.

A function in the form f(x) = ax² + bx + c , where a , b , and c are real numbers and a ≠ 0, that will graph as a parabola is known as:
a. first
b. second
c. quadratic
d. parabolic

Answer 1

The correct answer is 'c. quadratic'. The function f(x) = ax² + bx + c graphs as a parabola and is known as a quadratic function. The solution to these equations can be found using the quadratic formula.

Step-by-step explanation:

The correct answer to the question is c. quadratic. A function in the form f(x) = ax² + bx + c, where a, b, and c are real numbers and a ≠ 0, will graph as a parabola and is known as a quadratic function. These functions are also referred to as second-order polynomials due to the highest degree of the variable being 2. The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of the coefficient a.

Quadratic functions arise in many real-world situations, such as the trajectory of an object under gravity or the optimization of profit in business scenarios. The solution of quadratic equations can be found using the quadratic formula, which is applicable to any quadratic equation of the form ax²+bx+c = 0.