Understanding Quadratic Graphs

The video tutorial discusses the three possibilities for graphing quadratic equations: having two x-intercepts, one x-intercept, or no x-intercepts. It explains each scenario with examples, showing how the parabola interacts with the x-axis. The tutorial emphasizes that these concepts apply regardless of the parabola's orientation. The first example demonstrates a parabola with two x-intercepts, the second with one, and the third with none. The video concludes by summarizing these possibilities and their implications for solutions.

What are the three possibilities for the number of X intercepts in a quadratic graph?

• One, three, or four intercepts

• Zero, two, or three intercepts

• Zero, one, or two intercepts

• One, two, or three intercepts

In the first example, what are the X intercepts of the parabola?

• X = 3 and X = -2

• X = 2 and X = -3

• X = 1 and X = -1

• X = 4 and X = -4

What is the line of symmetry for the parabola in the first example?

• X = 3

• X = 1/2

• X = 0

• X = -2

In the second example, what is the factorized form of the quadratic equation?

• (x + 2)(x + 2)

• (x + 1)(x + 1)

• (x - 1)(x - 1)

• (x - 2)(x - 2)

How many X intercepts does the parabola have in the second example?

• Three

• Two

• One

• None

In the third example, why are there no X intercepts?

• The parabola is horizontal

• The equation has no real solutions

• The parabola is vertical

• The equation is linear

What is the value of Y when X is zero in the third example?

• Y = 5

• Y = 4

• Y = -4

• Y = 0

Which of the following describes a parabola with two X intercepts?

• The parabola touches the X-axis at one point

• The parabola crosses the X-axis at two points

• The parabola is parallel to the X-axis

• The parabola does not touch the X-axis

What happens when a parabola has its vertex on the X-axis?

• It has no X intercepts

• It has three X intercepts

• It has two X intercepts

• It has one X intercept

Which scenario results in a parabola with no X intercepts?

• The parabola opens upwards and crosses the X-axis

• The parabola opens downwards and is below the X-axis

• The parabola opens downwards and crosses the X-axis

• The parabola opens upwards and is above the X-axis