Key Features of Quadratics

Front

What are the zero(s) of a quadratic function?

Back

The zero(s) of a quadratic function are the values of x for which the function equals zero, also known as the roots or x-intercepts.

Front

What is the vertex of a quadratic function?

Back

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

Front

What does it mean if a quadratic function has a minimum?

Back

A quadratic function has a minimum if the parabola opens upwards, indicating the vertex is the lowest point.

Front

What does it mean if a quadratic function has a maximum?

Back

A quadratic function has a maximum if the parabola opens downwards, indicating the vertex is the highest point.

Front

What is the y-intercept of a quadratic function?

Back

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

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) for a quadratic in standard form.

Front

How do you find the roots of a quadratic equation?

Back

The roots can be found using factoring, completing the square, or the quadratic formula: x = (-b ± √(b²-4ac)) / (2a).

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants.

Front

What is the significance of the coefficient 'a' in a quadratic function?

Back

The coefficient 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

Front

What is the significance of the coefficient 'b' in a quadratic function?

Back

The coefficient 'b' affects the position of the vertex along the x-axis and influences the axis of symmetry.