Quadratic Functions Key Features Flashcard

Front

What is the range of a quadratic function that opens downwards?

Back

All real numbers less than or equal to the maximum value.

Front

What is the range of a quadratic function that opens upwards?

Back

All real numbers greater than or equal to the minimum value.

Front

What is the vertex of a quadratic function?

Back

The highest or lowest point on the graph of the function.

Front

How do you find the y-intercept of a quadratic function?

Back

Set x = 0 in the function and solve for y.

Front

What is the standard form of a quadratic function?

Back

y = ax^2 + bx + c, where a, b, and c are constants.

Front

What does the 'a' value in a quadratic function determine?

Back

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

Front

What is the axis of symmetry in a quadratic function?

Back

A vertical line that divides the parabola into two mirror-image halves, given by x = -b/(2a).

Front

What is the formula to find the vertex of a quadratic function in standard form?

Back

Vertex (h, k) where h = -b/(2a) and k = f(h).

Front

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

Back

It determines the nature of the roots: positive (two real roots), zero (one real root), negative (no real roots).

Front

What is the y-intercept of the function y = 2x^2 + 3x + 5?

Back

(0, 5) because when x = 0, y = 5.