Characteristics of Quadratic Functions

Front

What is the parent function of quadratic functions?

Back

Quadratic function

Front

What is the axis of symmetry in a quadratic function?

Back

A line whose equation is the x-coordinate of a parabola's vertex, dividing the parabola into mirror images.

Front

How do you identify the range of a quadratic function from its graph?

Back

The range is the set of possible y-values, often expressed as -6 ≤ y < ∞ for a parabola opening upwards.

Front

What is the y-intercept of a quadratic function?

Back

The point where the graph intersects the y-axis, e.g., (0, 2).

Front

What shape does the graph of a quadratic function take?

Back

The U-shaped graph of a quadratic function is called a parabola.

Front

What is the standard form of a quadratic function?

Back

The standard form is f(x) = ax² + bx + c, where a, b, and c are constants.

Front

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

Back

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

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its direction.

Front

How can you find the vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula x = -b/(2a) to find the x-coordinate, then substituting back to find the y-coordinate.

Front

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

Back

The discriminant (b² - 4ac) determines the number and type of roots: two real roots, one real root, or no real roots.