Domain, Range, and Key Features of Quadratics

Front

What is the definition of a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c.

Front

What does the term 'vertex' refer to in a quadratic function?

Back

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

Front

How can you determine the axis of symmetry for a quadratic function?

Back

The axis of symmetry can be found using the formula x = -b/(2a), where a and b are coefficients from the quadratic equation.

Front

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

Back

The discriminant (D = b² - 4ac) determines the number of real roots: D > 0 means 2 real roots, D = 0 means 1 real root, and D < 0 means no real roots.

Front

What is the range of a quadratic function that opens upwards?

Back

The range is all real numbers greater than or equal to the y-coordinate of the vertex.

Front

What is the range of a quadratic function that opens downwards?

Back

The range is all real numbers less than or equal to the y-coordinate of the vertex.

Front

How do you find the zeros of a quadratic function?

Back

Zeros can be found by setting the quadratic equation to zero and solving for x using factoring, completing the square, or the quadratic formula.

Front

What is the vertex form of a quadratic function?

Back

The vertex form is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

What does it mean for a quadratic function to have 'two zeros'?

Back

It means the graph of the quadratic intersects the x-axis at two distinct points.