Answer:
(c) y < x^2 -5x
Explanation:
A quadratic inequality is one that involves a quadratic polynomial.
Identification
The degree of a polynomial is the value of the largest exponent of the variable. When the degree of a polynomial is 2, we call it a quadratic.
For the following inequalities, the degree of the polynomial in x is shown:
- y < 2x +7 . . . degree 1
- y < x^3 +x^2 . . . degree 3
- y < x^2 -5x . . . degree 2 (quadratic)
Application
We see that the degree of the polynomial in x is 2 in ...
y < x^2 -5x
so that is the quadratic inequality you're looking for.
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Additional comment
When a term involves only one variable, its degree is the exponent of that variable: 5x^3 has degree 3. When a term involves more than one variable, the degree of the term is the sum of the exponents of the variables: 8x^4y3 has degree 4+3=7.