Characteristics of Quadratics

Front

What is another term for the roots of a quadratic function?

Back

Zeros

Front

What is the interval where a quadratic function is decreasing if it has a vertex at (h,k)?

Back

(h, ∞) where h is the x-coordinate of the vertex.

Front

What is the interval where a quadratic function is increasing if it has a vertex at (h,k)?

Back

(-∞, h) where h is the x-coordinate of the vertex.

Front

What is the axis of symmetry for a parabola with vertex at (h,k)?

Back

x = h

Front

What is the domain of a quadratic function?

Back

All Real Numbers (-∞, ∞)

Front

How do you find the vertex of a quadratic function in standard form y = ax^2 + bx + c?

Back

Use the formula h = -b/(2a) for the x-coordinate and substitute h back into the function to find k.

Front

What does the 'a' value in the quadratic equation y = ax^2 + bx + c determine?

Back

The direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b^2 - 4ac) determines the nature of the roots: two real roots if > 0, one real root if = 0, and no real roots if < 0.

Front

What is the vertex form of a quadratic function?

Back

y = a(x - h)^2 + k, where (h,k) is the vertex.

Front

How can you determine if a quadratic function opens upwards or downwards?

Back

By the sign of the coefficient 'a': if a > 0, it opens upwards; if a < 0, it opens downwards.