Factoring Quadratic Expressions and Functions

This video tutorial explains how to factor quadratic expressions of the form ax² + bx + c by identifying common factors using the graph of the related quadratic function. It demonstrates the process with two examples, showing how to determine the zeros of the function and write the expression in factored form. The tutorial also includes a step-by-step guide on using a TI-84 calculator to verify intercepts and adjust graph settings for better visualization.

What is the purpose of finding the zeros of a quadratic function when factoring?

• To find the maximum value of the function

• To calculate the slope of the function

• To determine the y-intercepts

• To write the quadratic in factored form

Which of the following is a step in factoring a quadratic expression using its graph?

• Determining the axis of symmetry

• Calculating the vertex

• Identifying the horizontal intercepts

• Finding the y-intercepts

In the expression 2x^2 + 14x - 36, what are the zeros found from the graph?

• x = -9 and x = 2

• x = 0 and x = 14

• x = -14 and x = 36

• x = 9 and x = -2

What is the factored form of 2x^2 + 14x - 36?

• (x + 9)(x - 2)

• 2(x - 9)(x + 2)

• (x - 9)(x + 2)

• 2(x + 9)(x - 2)

What are the horizontal intercepts of the graph for 6x^2 - 39x + 54?

• (2, 0) and (4.5, 0)

• (3, 0) and (5, 0)

• (1, 0) and (6, 0)

• (0, 0) and (7, 0)

What is the coefficient of x^2 in the expression 6x^2 - 39x + 54?

• 54

• 39

• 6

• 0

How can you verify the intercepts of a quadratic function using a calculator?

• By solving the quadratic equation

• By using the zoom function

• By calculating the derivative

• By using the graphing function

What is the purpose of adjusting the graph view when analyzing a quadratic function?

• To better visualize the intercepts

• To increase the graph's size

• To change the function's equation

• To alter the function's zeros

What is the factored form of 6x^2 - 39x + 54 after clearing fractions?

• 2(3x - 9)(x + 2)

• 6(x - 2)(x - 9/2)

• 3(x - 9)(x + 2)

• 3(2x - 9)(x - 2)

Why is it beneficial to clear fractions in the factored form of a quadratic expression?

• To change the zeros of the function

• To increase the degree of the polynomial

• To simplify calculations

• To make the expression more complex