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.

Tags

CCSS.HSF-IF.C.7C

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.

Tags

CCSS.HSF-IF.C.7C

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.

Tags

CCSS.8.F.A.1

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.

Tags

CCSS.HSA.APR.C.4

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.

Tags

CCSS.HSF-IF.C.7A

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B