Quadratics

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 equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

Front

How do you find 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 nature of the roots: if D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

Front

What are the zeros of a quadratic function?

Back

The zeros of a quadratic function are the values of x that make the function equal to zero, also known as the roots of the equation.

Front

How can you find the zeros of a quadratic equation in factored form?

Back

To find the zeros of a quadratic equation in factored form (x - p)(x - q) = 0, set each factor equal to zero: x - p = 0 and x - q = 0.

Front

What does it mean for a quadratic function to have a maximum or minimum value?

Back

A quadratic function has a maximum value if it opens downwards (a < 0) and a minimum value if it opens upwards (a > 0).

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

How do you convert a quadratic function from standard form to vertex form?

Back

To convert from standard form to vertex form, complete the square on the quadratic expression.