Characteristics of a Quadratic Function

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. It passes through the vertex of the parabola.

Front

What is the vertex of a quadratic function?

Back

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

Front

How do you find the x-intercepts of a quadratic function?

Back

The x-intercepts can be found by setting the quadratic equation equal to zero and solving for x. They are the points where the graph intersects the x-axis.

Front

What is a parabola?

Back

A parabola is the graph of a quadratic function, which is a U-shaped curve that can open upwards or downwards.

Front

What does it mean if a parabola opens upwards?

Back

If a parabola opens upwards, it means that the vertex is the minimum point of the function, and the arms of the parabola extend upwards.

Front

What does it mean if a parabola opens downwards?

Back

If a parabola opens downwards, it means that the vertex is the maximum point of the function, and the arms of the parabola extend downwards.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

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

How can you determine the number of x-intercepts from the quadratic equation?

Back

The number of x-intercepts can be determined using the discriminant (b^2 - 4ac). If it's positive, there are two x-intercepts; if zero, one; if negative, none.

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.