A quadratic equation graphs as a parabola. Which statement is true?

A quadratic equation graphs as a parabola. Which statement is true?

• A. It has a constant rate of change
• B. It is linear
• C. It can have up to two x-intercepts
• D. It never crosses the x-axis

Answer: (C)

A quadratic graph is a parabola, and a key property is that it can cross the x-axis at most twice. This comes from solving ax^2 + bx + c = 0: there are at most two real solutions, depending on the discriminant (two solutions if it’s positive, one if it’s zero, none if it’s negative). So the statement that it can have up to two x-intercepts is true. The other statements aren’t generally correct: the rate of change for a quadratic isn’t constant—the slope changes with x (the derivative is 2ax + b). It isn’t a linear graph; it’s a curved parabola. And while a parabola can cross the x-axis two times or just touch it once or not at all, it doesn’t categorically never cross the x-axis.

A quadratic graph is a parabola, and a key property is that it can cross the x-axis at most twice. This comes from solving ax^2 + bx + c = 0: there are at most two real solutions, depending on the discriminant (two solutions if it’s positive, one if it’s zero, none if it’s negative). So the statement that it can have up to two x-intercepts is true.

The other statements aren’t generally correct: the rate of change for a quadratic isn’t constant—the slope changes with x (the derivative is 2ax + b). It isn’t a linear graph; it’s a curved parabola. And while a parabola can cross the x-axis two times or just touch it once or not at all, it doesn’t categorically never cross the x-axis.