How is a linear equation different from a quadratic equation?

How is a linear equation different from a quadratic equation?

• A. It uses numbers only
• B. It has more than one variable
• C. It is solved by factoring
• D. It has degree 1 and produces a straight line; a quadratic has degree 2 and produces a parabola

Answer: (D)

The important idea here is that the degree of a polynomial—the highest exponent on the variable—determines the basic shape you’ll see when you graph it. If the equation is linear, the variable only appears to the first power, so its graph is a straight line with constant slope. If the equation is quadratic, you have a squared term, making the graph bend and form a parabola. The number of variables or the method you use to solve it aren’t what define linear versus quadratic; it’s the degree and the resulting shape: degree 1 gives a straight line, degree 2 gives a parabola.

The important idea here is that the degree of a polynomial—the highest exponent on the variable—determines the basic shape you’ll see when you graph it. If the equation is linear, the variable only appears to the first power, so its graph is a straight line with constant slope. If the equation is quadratic, you have a squared term, making the graph bend and form a parabola. The number of variables or the method you use to solve it aren’t what define linear versus quadratic; it’s the degree and the resulting shape: degree 1 gives a straight line, degree 2 gives a parabola.