Characteristics of Quadratics

Front

What is a quadratic function?

Back

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

Front

What is the shape of the graph of a quadratic function?

Back

The graph of a quadratic function is called a parabola.

Front

What is the vertex of a parabola?

Back

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

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, passing through the vertex.

Front

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

Back

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

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

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

Back

It means that the graph of the function does not intersect the x-axis, indicating that the parabola is entirely above or below the x-axis.

Front

What is the standard form of a quadratic function?

Back

The standard form is f(x) = ax² + bx + c.

Front

What is the vertex form of a quadratic function?

Back

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