Graphing 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 does the graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of the coefficient 'a'.

Front

What is the vertex of a parabola?

Back

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

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) and then substituting this x-value back into the function to find the y-coordinate.

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 are x-intercepts?

Back

X-intercepts are the points where the graph of a function crosses the x-axis, which occur when f(x) = 0.

Front

What is another name for x-intercepts?

Back

Zeros.

Front

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

Back

The maximum or minimum value is the y-coordinate of the vertex, representing the highest or lowest point of the graph.

Front

How can you determine if a quadratic function has a maximum or minimum?

Back

If the coefficient 'a' is positive, the parabola opens upwards and has a minimum. If 'a' is negative, it opens downwards and has a maximum.

Front

What does it mean if a quadratic function has no x-intercepts?

Back

It means the graph does not cross the x-axis, indicating that the quadratic has no real solutions.