Factoring Quadratics and Graphing Concepts

The video tutorial explains how to factor basic quadratic expressions of the form ax^2 + bx + c, where a equals one, using the graph of the corresponding quadratic function. It covers determining zeros by finding x-intercepts and discusses three possible graph outcomes: two distinct intercepts, one intercept (double zero), or no intercepts. The tutorial includes examples of factoring x^2 - 2x - 8 and x^2 - 8x + 15 using a TI-84 graphing calculator.

What is the form of a basic quadratic expression that is being factored in this video?

• ax^2 + bx + c where a = 2

• ax^2 + bx + c where a = 1

• ax^2 + bx + c where a = 0

• ax^2 + bx + c where a = -1

Tags

CCSS.HSF-IF.C.8A

CCSS.HSA-SSE.B.3B

What are the zeros of a quadratic function?

• The y-values that make the function zero

• The x-values that make the function zero

• The points where the graph is vertical

• The points where the graph is horizontal

Tags

CCSS.HSF-IF.C.7A

What does it mean if a quadratic graph has no horizontal intercepts?

• The function has complex zeros

• The function has no real zeros

• The function has one real zero

• The function has two real zeros

Tags

CCSS.HSF-IF.C.8A

CCSS.HSA-SSE.B.3B

How can you determine the zeros of a quadratic function using a graphing calculator?

• By identifying the horizontal intercepts

• By calculating the slope

• By measuring the distance between points

• By finding the vertex

What is the factored form of x^2 - 2x - 8?

• (x - 4)(x + 2)

• (x + 4)(x - 2)

• (x - 2)(x + 4)

• (x + 2)(x - 4)

Tags

CCSS.HSF-IF.C.7A

What is the significance of a double zero in a quadratic graph?

• It indicates a single zero with multiplicity two

• It indicates two distinct zeros

• It indicates complex zeros

• It indicates no zeros

Tags

CCSS.HSF-IF.C.7A

What is the first step in graphing a quadratic function on a TI-84 calculator?

• Pressing the 'Graph' button

• Adjusting the window settings

• Entering the function in 'Y='

• Calculating the intercepts

Tags

CCSS.HSF-IF.C.7A

What does the standard window setting on a graphing calculator help you see?

• The vertex of the graph

• The y-intercept

• The slope of the graph

• The horizontal intercepts

What is the factored form of x^2 - 8x + 15?

• (x + 5)(x - 3)

• (x - 5)(x + 3)

• (x - 3)(x - 5)

• (x + 3)(x + 5)

Why is it useful to factor a quadratic expression?

• To find the slope of the graph

• To determine the y-intercept

• To verify the original expression

• To calculate the area under the curve