Characteristics of Quadratics Graphs

Front

What is the vertex of a quadratic graph?

Back

The vertex is the highest or lowest point on the graph of a quadratic function, represented as a coordinate (h, k).

Front

What are the x-intercepts of a quadratic graph?

Back

The x-intercepts are the points where the graph crosses the x-axis, represented as coordinates (x, 0).

Front

How do you identify the roots of a quadratic function?

Back

The roots are the values of x for which the quadratic function equals zero, often found using factoring, completing the square, or the quadratic formula.

Front

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

Back

A maximum value occurs at the vertex of the graph when the parabola opens downwards, indicating the highest point on the graph.

Front

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

Back

A minimum value occurs at the vertex of the graph when the parabola opens upwards, indicating the lowest point on the graph.

Front

What is the axis of symmetry in a quadratic graph?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, passing through the vertex.

Front

How can you determine if a quadratic function opens upwards or downwards?

Back

If the leading coefficient (a) is positive, the parabola opens upwards; if negative, it opens downwards.

Front

What is the standard form of a quadratic function?

Back

The standard form is written as 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 width and direction of the parabola; larger absolute values of 'a' make the parabola narrower.

Front

What is the quadratic formula used for?

Back

The quadratic formula, x = (-b ± √(b² - 4ac)) / (2a), is used to find the roots of a quadratic equation.