Question

Okay so I had this question and I am so confuso!!!

Compare and contrast the two quadratic equations below. In order to receive full credit, use complete sentences to describe the following:

The direction each parabola opens
The vertex of each parabola
y = x2 − 2x
y = −2x2 + 4x − 3

I don't want you to help me with the question I need to know if the first equation is right?

Answer 1

Because I thought a quadratic equation had to have 3 terms not 2

Answer 2

If we talk about a parabola generally, say in the form \(y = ax^2 + bx + c\), the sign of \(a\) (i.e., positive or negative) determines whether it is concave up or concave down. Also, the vertex of such a parabola is its intersection with the vertical line \(x=-\dfrac{b}{2a}\).

Answer 3

Yes but the first equation only has 2 terms not 3

Answer 4

A quadratic equation can most certainly have two terms. It need only be a polynomial in \(x\) such that its highest power is \(x^2\) to be quadratic.

Answer 5

@JA1 - that just means that \(b\) or \(c\) is zero.

Answer 6

So y = x2 − 2x is a Quadratic?

Answer 7

Most certainly!