Factored Form of Quadratic Functions

Front

What is the factored form of a quadratic function?

Back

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

Front

What does GCF stand for in mathematics?

Back

GCF stands for Greatest Common Factor, which is the largest positive integer that divides all the given numbers without leaving a remainder.

Front

How do you find the GCF of two or more numbers?

Back

To find the GCF, list the factors of each number, identify the common factors, and select the largest one.

Front

What is the GCF of 8, 12, and 20?

Back

The GCF of 8, 12, and 20 is 4.

Front

Factor out the GCF from 3x + 9.

Back

3(x + 3)

Front

Factor out the GCF from 10x² - 15x + 25.

Back

5(2x² - 3x + 5)

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Factor out the GCF from 4x³ - 2x² + 6x.

Back

2x(2x² - x + 3)

Front

What are the steps to factor a quadratic expression?

Back

1. Identify the GCF. 2. Rewrite the expression as a product of the GCF and the remaining polynomial. 3. Factor the remaining polynomial if possible.

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.

Front

What is the significance of the roots in a quadratic function?

Back

The roots of a quadratic function are the x-values where the function intersects the x-axis, indicating the solutions to the equation f(x) = 0.