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 are the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph of the function crosses the x-axis, found by solving the equation f(x) = 0.

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph crosses the y-axis, found by evaluating the function at x = 0.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point on the graph of the quadratic function, depending on the direction of the parabola.

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

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

Back

The range is all real numbers greater than or equal to the y-coordinate of the vertex.

Front

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

Back

The range is all real numbers less than or equal to the y-coordinate of the vertex.

Front

How do you determine if a quadratic function has real roots?

Back

You can determine this by calculating the discriminant (D = b² - 4ac). If D > 0, there are two real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

Front

What does it mean for a vertex to be a maximum or minimum?

Back

A vertex is a maximum if the parabola opens downwards (a < 0) and a minimum if it opens upwards (a > 0).

Front

What is the standard form of a quadratic function?

Back

The standard form is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.