Question

Hi,

I'm trying to understand what a quadratic equation is. I understand that in a quadratic equation you have to have a variable in the second power. Why, then, aren't y = x^2 + 2x^3 and Y = 2x^2 + 3 times the square root of x quadratic equations? They both have powers of x that are squared.

Answer 1

Small change to your definition.
The highest power must be a square term.

The degree of a polynomial is determined by the highest power, so in your case you would have a cubic because of the x^3 term

a quadratic must have the form
y = ax^2 + bx + c, where the a,b, and c are constants except a ≠ 0, but b and c could be zero

examples of quadratics
y = x^2
y = 3.4x^2 - 99x + π
y = -2x^2 - 6x
y = x^2 + 1

Answer 2

Thank you, Reiny, however, why wouldn't my second example, y = 2x^2 + 3 times the square root of x be a quadratic equation since the highest power would be 2?

Answer 3

Your second equation IS a quadratic function.
since the highest power you see is x^2.
Sorry if you misunderstood.

btw, don't say "square root of x", that would be √x
the term is "x squared"

Answer 4

The answer book says that this one is NOT a quadratic equation.

It looks like y = 2x^2 + 3 and then what you typed - I'm not able to type that. Isn't that three times the square root of x?