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.
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
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?
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"
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?
Hello!
You're on the right track understanding that a quadratic equation involves a variable raised to the power of 2. However, there is a key distinction between quadratic equations and equations with higher powers or non-integer powers.
In a quadratic equation, the variable is only raised to the power of 2. This means that the highest power of the variable in a quadratic equation is 2, and any other powers of the same variable should not exceed the power of 2.
So, let's take a closer look at the examples you provided:
1. y = x^2 + 2x^3
In this equation, you have the variable x raised to the power of 2 (x^2) and also raised to the power of 3 (x^3). This makes it a cubic equation, not a quadratic equation. Cubic equations involve the variable raised to the power of 3 or cube numbers.
2. Y = 2x^2 + 3√x
In this equation, the variable x is raised to the power of 2 (x^2), which is correct for a quadratic term. However, the second term is the square root of x (√x), not x raised to a power of 2. Thus, it is not a quadratic term. It is important for all terms in a quadratic equation to have the variable raised to the power of 2.
To summarize, a quadratic equation involves the variable raised to the power of 2, and other powers or non-integer powers are not included in the quadratic equation.