Quadratic Functions Review

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically 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 function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola represented by the quadratic function, found at the point (h, k) in the vertex form f(x) = a(x-h)² + k.

Front

How do you find the vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula h = -b/(2a) and k = f(h).

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, given by the equation x = h, where h is the x-coordinate of the vertex.

Front

What are the roots of a quadratic function?

Back

The roots (or solutions) are the values of x where the quadratic function equals zero, found by solving the equation ax² + bx + c = 0.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, b² - 4ac, which determines the nature of the roots.

Front

What does it mean if the discriminant is positive?

Back

If the discriminant is positive, the quadratic equation has two distinct real roots.

Front

What does it mean if the discriminant is zero?

Back

If the discriminant is zero, the quadratic equation has exactly one real root (a repeated root).