Key Features from Graphs of Quadratic Functions

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.

Front

What does the term 'axis of symmetry' refer to in a quadratic function?

Back

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

Front

How can you determine the direction of opening of a parabola?

Back

If the coefficient of the x^2 term is positive, the parabola opens upwards; if negative, it opens downwards.

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 does it mean if a quadratic function has no real solutions?

Back

It means the graph does not intersect the x-axis, indicating that the vertex is above (for upward-opening) or below (for downward-opening) the x-axis.

Front

What is the standard form of a quadratic function?

Back

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

Front

How do you find the x-coordinate of the vertex in standard form?

Back

The x-coordinate of the vertex can be found using the formula x = -b/(2a).

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by b^2 - 4ac, which determines the nature of the roots.

Front

What does a positive discriminant indicate?

Back

A positive discriminant indicates that the quadratic equation has two distinct real solutions.

Front

What does a zero discriminant indicate?

Back

A zero discriminant indicates that the quadratic equation has exactly one real solution (a repeated root).