Quadratic Functions Key Features Warmup

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 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 '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) to find the x-coordinate, and then substituting this 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 is the significance of the y-intercept in 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 significance of the x-intercepts in a quadratic function?

Back

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

Front

What is the difference between maximum and minimum values in a quadratic function?

Back

A maximum value occurs at the vertex of a downward-opening parabola, while a minimum value occurs at the vertex of an upward-opening parabola.

Front

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

Back

You can determine this by looking at the coefficient 'a': if 'a' is positive, the function has a minimum; if 'a' is negative, it has a maximum.