Understanding Quadratic Functions

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 shape does the graph of a quadratic function take?

Back

The graph of a quadratic function is a parabola.

Front

What determines whether a parabola opens upwards or downwards?

Back

The sign of the coefficient 'a' in the quadratic function determines the direction: if a > 0, the parabola opens upwards; if a < 0, it opens downwards.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens downwards or upwards.

Front

How do you find the axis of symmetry of a parabola?

Back

The axis of symmetry of a parabola can be found using the formula x = -b/(2a), where a and b are the coefficients from the quadratic equation in standard form.

Front

What is the significance of the axis of symmetry in a parabola?

Back

The axis of symmetry divides the parabola into two mirror-image halves and passes through the vertex.

Front

What is the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value of a quadratic function occurs at the vertex. If the parabola opens downwards, the vertex represents the maximum value; if it opens upwards, it represents the minimum value.

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 is the vertex form of a quadratic function?

Back

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

Front

How can you determine the y-intercept of a quadratic function?

Back

The y-intercept of a quadratic function can be found by evaluating the function at x = 0, which gives the point (0, c) in the standard form.