Question

If f(x) and g(x) are quadratic functions but (f + g)(x) produces the graph below, which statement must be true?

On a coordinate plane, a straight line with negative slope represents (f + g) (x). It goes through points (negative 3, 4), (0, 1), and (1, 0).
The leading coefficients of f(x) and g(x) are opposites.
The leading coefficients of f(x) and g(x) are opposite reciprocals.
The leading coefficients of f(x) and g(x) are the same.
The leading coefficients of f(x) and g(x) are reciprocals.

Answer 1

The missing graph is attached down

The true statement must be " The leading coefficients of f(x) and g(x) are opposites " ⇒ 1st answer

Step-by-step explanation:

Let us revise some important notes

• The greatest power of the linear function is one
• The greatest power of the quadratic function is two
• The leading coefficient of a function is the coefficient of the greatest power term

∵ f(x) and g(x) are quadratic functions

∴ The greatest power of them is two

∴ The leading coefficient is the coefficient of x²

From the attached graph below

∵ (f + g)(x) is represented by a line

∴ (f + g)(x) is a linear function

∴ The greatest power of it is one

- That means the terms of x² in f(x) and g(x) canceled each other,

   then the sum of their coefficients = 0, so their coefficients must

   be equal in values and different in signs

∴ The leading coefficients of f(x) and g(x) are opposites

The true statement must be " The leading coefficients of f(x) and g(x) are opposites "

Learn more:

You can learn more about the quadratic functions in brainly.com/question/1332667

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Answer 2

Answer:

leading coefficients are opposites

Step-by-step explanation: