Quadratic Equations and Functions

Question

Explain what you can determine about the shape of a parabola from its equation alone.

Answer 1

You can determine how a parabola opens as well as how it stretches.

 

Opens upward if the leading coefficient is positive.

Opens downward if the leading coefficient is negative.

 

Stretches vertically (becomes more narrow) when the leading coefficient increases.

Stretches horizontally (becomes more wider) when the leading coefficient decreases.

Parabola becomes a straight line when leading coefficient is zero.

Parabola becomes a horizontal line when all coefficients of xⁿ , with n≥0, is zero.