DETERMINE IF A FUCNTION IS LINEAR QUADRATIC OR CONSTANT

Determine whether each function is linear or quadratic. Identify the quadratic, linear, and constant terms.

Problem 1 :

y = (x – 2)(x + 4)

Solution :

It is in factored form.

y = x² + 4x - 2x - 8

y = x² + 2x - 8

The degree of the polynomial is 2. So, it is quadratic.

Problem 2 :

y = 3x(x + 5)

Solution :

y = 3x(x + 5)

Distributing 3x, we get

y = 3x² + 15x

Degree of the polynomial is 2. So, it is quadratic polynomial.

Problem 3 :

y = 5x(x – 5) –5x²

Solution :

y = 5x(x – 5) –5x²

y = 5x² – 5x –5x²

By combining the like terms, we get

y = – 5x

Degree of this polynomial is 1. So, it is a linear.

Problem 4 :

f(x) = 7(x – 2) + 5(3x)

Solution :

f(x) = 7(x – 2) + 5(3x)

f(x) = 7x - 14 + 15x

By combining the like terms

f(x) = 22x - 14

The degree of the polynomial is 1. So it is linear.

Problem 5 :

f(x) = 3x² – (4x – 8)

Solution :

f(x) = 3x² – (4x – 8)

f(x) = 3x² – 4x + 8

Degree of the f(x) is 2. So, it is quadratic polynomial.

Problem 6 :

y = 3x(x – 1) – (3x + 7)

Solution :

y = 3x(x – 1) – (3x + 7)

y = 3x² - 3x - 3x - 7

By combining the like terms, we get

y = 3x² - 6x - 7

The degree of the polynomial is 2. So, it is quadratic.

Problem 7 :

y = 3x² – 12

Solution :

The degree of the polynomial is 2. So, it is quadratic.

Problem 8 :

f(x) = (2x – 3)(x + 2) 

Solution :

The degree of the polynomial is 2. So, it is quadratic.