Quadratics Review

Front

What is 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 ax² + bx + c = 0, where a, b, and c are constants.

Front

What are the zeros of a quadratic function?

Back

The zeros of a quadratic function are the values of x for which f(x) = 0. They are also known as the roots of the equation.

Front

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

Back

The vertex (h, k) of a quadratic function in standard form f(x) = ax² + bx + c can be found using the formula h = -b/(2a) and k = f(h).

Front

What is the vertex form of a quadratic function?

Back

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

Front

What does the 'a' value in a 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 axis of symmetry in a quadratic function?

Back

The axis of symmetry of a quadratic function 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

How do you determine the range of a quadratic function?

Back

The range of a quadratic function can be determined by identifying the vertex and the direction of the parabola. If the parabola opens upward, the range is [k, ∞) and if it opens downward, the range is (-∞, k].

Front

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

Back

The discriminant (D = b² - 4ac) indicates the nature of the roots of a quadratic equation: D > 0 means two distinct real roots, D = 0 means one real root, and D < 0 means no real roots.

Front

What is the factored form of a quadratic function?

Back

The factored form of a quadratic function is f(x) = a(x - r₁)(x - r₂), where r₁ and r₂ are the roots of the function.