Finding the Zeros/Factoring

Front

What is the process of factoring a quadratic expression?

Back

Factoring a quadratic expression involves rewriting it as a product of two binomials, typically in the form (x + p)(x + q), where p and q are numbers that satisfy the equation.

Front

How do you find the zeros of a quadratic function?

Back

To find the zeros of a quadratic function, set the function equal to zero and solve for x. This can often be done by factoring, using the quadratic formula, or completing the square.

Front

What are the zeroes of the function f(x) = (x - 7)(x + 8)?

Back

The zeroes of the function are x = 7 and x = -8.

Front

What is a quadratic expression?

Back

A quadratic expression is a polynomial of degree 2, typically in the form ax^2 + bx + c, where a, b, and c are constants.

Front

What does it mean for a table to represent a function?

Back

A table represents a function if each input (x-value) corresponds to exactly one output (y-value). If an input has multiple outputs, it is not a function.

Front

What is the factored form of the quadratic expression x^2 + 11x + 24?

Back

The factored form is (x + 8)(x + 3).

Front

What is the factored form of the quadratic expression d^2 - 10d + 25?

Back

The factored form is (d - 5)(d - 5), or (d - 5)^2.

Front

What is the significance of the coefficients in a quadratic expression?

Back

The coefficients a, b, and c in a quadratic expression ax^2 + bx + c determine the shape and position of the parabola represented by the quadratic function.

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, and what does it indicate?

Back

The discriminant is the part of the quadratic formula under the square root, b² - 4ac. It indicates the nature of the roots: if positive, there are two distinct real roots; if zero, one real root; if negative, two complex roots.