Features of Quadratics Review

Front

What is the domain of a quadratic function?

Back

The domain of any quadratic function is all real numbers.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the point where the graph changes direction, represented as (h, k) in the vertex form f(x) = a(x - h)² + k.

Front

How do you find the line of symmetry for a quadratic function?

Back

The line of symmetry for a quadratic function is given by the equation x = h, where (h, k) is the vertex of the parabola.

Front

What does the 'a' value in the quadratic function indicate?

Back

The 'a' value in a quadratic function determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

Front

What is the range of a quadratic function with a maximum vertex?

Back

The range of a quadratic function with a maximum vertex is all real numbers less than or equal to the y-coordinate of the vertex.

Front

What is the range of a quadratic function with a minimum vertex?

Back

The range of a quadratic function with a minimum vertex is all real numbers greater than or equal to the y-coordinate of the vertex.

Front

What is the quadratic formula used for?

Back

The quadratic formula is used to find the roots (solutions) of a quadratic equation in the form ax² + bx + c = 0, given by x = (-b ± √(b² - 4ac)) / (2a).

Front

What does the discriminant of a quadratic equation tell us?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if positive, there are two distinct real roots; if zero, there is one real root; if negative, there are two complex roots.

Front

What is the effect of changing the 'b' value in a quadratic function?

Back

Changing the 'b' value in a quadratic function affects the position of the vertex and the line of symmetry but does not change the direction of the parabola.