Is this a quadratic or linear function? Identify the quadratic,linear, and constant terms
3(x-2)^2+12x
If you have an x^2 term in the function, it is quadratic.
Once you have simplified the function, the numerical value for x^2 is quadratic, the numerical value for x is linear, and other numbers are constants.
(x-2)^2 = x^2 - 4x + 4
3x^2 - 12x + 12 + 12x = 3x^2 + 12
I hope this helps. Thanks for asking.
The given expression is a quadratic function.
The quadratic term is 3(x-2)^2,
the linear term is 12x,
and there is no constant term in this equation.
To determine whether the given expression is a quadratic or linear function and identify the quadratic, linear, and constant terms, we need to understand the structure of the expression.
A quadratic function is a polynomial function of degree 2, which means its highest exponent is 2. A linear function, on the other hand, is a polynomial function of degree 1, with the highest exponent being 1. A constant term is a term that does not contain any variables.
Let's examine the given expression and identify its different terms:
3(x-2)^2 + 12x
In this expression:
- The term 3(x-2)^2 represents the quadratic term since it has the highest exponent, 2. This term is obtained by squaring the quantity (x-2).
- The term 12x represents the linear term since it has the highest exponent, 1, and it contains the variable x.
- There is no term without a variable, so there are no constant terms in this expression.
Therefore, the given expression is a quadratic function, and its quadratic term is 3(x-2)^2, while its linear term is 12x.