Characteristics of Quadratics

Front

What are the x-intercepts of a quadratic function?

Back

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

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 can be found using the formula x = -b/(2a) for a quadratic in the form ax^2 + bx + c.

Front

What is the shape of the graph of a quadratic function called?

Back

The graph of a quadratic function is called a parabola.

Front

What is the maximum or minimum point of a quadratic function called?

Back

The maximum or minimum point of a quadratic function is called the vertex.

Front

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

Back

A quadratic function opens upwards if the coefficient of x^2 (a) is positive, and it opens downwards if a is negative.

Front

What is the vertex of a quadratic function in standard form?

Back

The vertex of a quadratic function in standard form (y = ax^2 + bx + c) can be found using the formula (h, k) where h = -b/(2a) and k = f(h).

Front

What does the term 'discriminant' refer to in a quadratic equation?

Back

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

Front

What does a positive discriminant indicate about the roots of a quadratic equation?

Back

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

Front

What does a zero discriminant indicate about the roots of a quadratic equation?

Back

A zero discriminant indicates that the quadratic equation has exactly one real root, also known as a repeated or double root.

Front

What does a negative discriminant indicate about the roots of a quadratic equation?

Back

A negative discriminant indicates that the quadratic equation has no real roots, but two complex roots.