Key Features of quadratic functions

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c.

Front

What are the key features of a quadratic function?

Back

Key features include the vertex, axis of symmetry, x-intercepts (zeros), y-intercept, and the direction of the parabola (opening up or down).

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its direction. It can be found using the formula (-b/2a, f(-b/2a)).

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = -b/2a.

Front

How do you find the x-intercepts of a quadratic function?

Back

The x-intercepts can be found by setting f(x) = 0 and solving the equation ax² + bx + c = 0.

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, found by evaluating f(0) = c.

Front

What does it mean if a quadratic function has two real zeros?

Back

It means the graph intersects the x-axis at two points, indicating two distinct solutions to the equation f(x) = 0.

Front

What does it mean if a quadratic function has one real zero?

Back

It means the graph touches the x-axis at one point (the vertex), indicating a repeated solution to the equation f(x) = 0.

Front

What does it mean if a quadratic function has no real zeros?

Back

It means the graph does not intersect the x-axis, indicating that the solutions to the equation f(x) = 0 are complex numbers.