Characteristics of Quadratic Graphs

Front

What is the vertex of a quadratic graph?

Back

The vertex is the highest or lowest point of the graph, depending on its orientation.

Front

What are the coordinates of the y-intercept in a quadratic function?

Back

The y-intercept is the point where the graph crosses the y-axis, represented as (0, y).

Front

Describe the shape of a quadratic function.

Back

A quadratic function has a U-shaped graph.

Front

What does it mean if a quadratic graph is concave up?

Back

If a quadratic graph is concave up, it opens upwards and the vertex is the minimum point.

Front

What does it mean if a quadratic graph is concave down?

Back

If a quadratic graph is concave down, it opens downwards and the vertex is the maximum point.

Front

How can you determine the direction of a quadratic graph's opening?

Back

The direction can be determined by the sign of the leading coefficient (a) in the quadratic equation y = ax^2 + bx + c.

Front

What is the standard form of a quadratic equation?

Back

The standard form is y = ax^2 + bx + c.

Front

What is the axis of symmetry in a quadratic graph?

Back

The axis of symmetry is a vertical line that divides the graph into two mirror-image halves, given by x = -b/(2a).

Front

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

Back

The x-intercepts can be found by solving the equation ax^2 + bx + c = 0.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b^2 - 4ac) determines the nature of the roots: two real roots, one real root, or no real roots.