Respuesta :
The given function is quadratic. The quadratic term is -18x², the linear term is 39x, and the constant term is -20. So, first option is correct.
What is a quadratic function?
A function in which the highest degree of the variable is 2, then that function is said to be a quadratic function.
The general form of a quadratic function is ax² + bx + c. Where the terms are:
ax² - quadratic term;
bx - linear term;
c - constant term;
What is a linear function?
A function in which the highest degree of the variable is 1, then that function is said to be a linear function.
The general form of a linear function is ax + c. Where the terms are:
ax - linear term;
c - constant term;
Expanding the given function:
The given function is f(x) = (3x - 4)(-6x + 5)
Expanding the given function,
f(x) = (3x)(-6x) + (3x)(5) + (-4)(-6x) + (-4)(5)
= -18x² + 15x + 24x - 20
= -18x² + 39x - 20
Since the highest degree of the variable x in the obtained function is 2, it is a quadratic function.
The terms in the obtained quadratic function are:
quadratic term: -18x²
linear term: 39x
constant term: -20
Therefore, the first option is correct.
Learn more about quadratic function here:
https://brainly.com/question/11631534
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Disclaimer: The question has a mistake in the function. The corrected question is here.
Question: Determine whether the function is linear or quadratic. Identify the quadratic, linear, and constant terms.
f(x)= (3x - 4)(-6x + 5)
