Graph Analysis and Transformations

The video tutorial explains the concept of zeros and roots in quadratic equations, focusing on where the parabola intersects the x-axis. It guides viewers on identifying solutions from tables and determining true or false statements about graph properties. The tutorial also covers matching graphs to tables, translating graphs, and analyzing graph solutions by extending parabolas.

What is another term for the zeros of a quadratic equation?

• Intercepts

• Coefficients

• Vertices

• Roots

Where are the roots of a quadratic equation located on its graph?

• At the vertex

• At the axis of symmetry

• Where it crosses the x-axis

• At the y-intercept

If a parabola crosses the x-axis at two points, what does this indicate?

• It has two real solutions

• It has no real solutions

• It has one real solution

• It has complex solutions

In a table of values, what y-value indicates an x-intercept?

• 1

• 0

• Any positive number

• -1

What does it mean if two graphs have the same axis of symmetry?

• They are symmetric about the same line

• They are reflections

• They are identical

• They have the same roots

What does a minimum point on a graph indicate?

• The point where the graph crosses the x-axis

• The point where the graph crosses the y-axis

• The highest point of the graph

• The lowest point of the graph

If a graph has two high points, what does this suggest about its shape?

• It is a linear function

• It is a parabola

• It is a hyperbola

• It is a cubic function

What does it mean if two functions have different y-intercepts?

• They are identical

• They intersect at the same point

• They have the same slope

• They start at different points on the y-axis

How can you determine if a graph has a minimum or maximum point?

• By analyzing the slope

• By checking the x-intercepts

• By analyzing the vertex

• By checking the y-intercepts

What does it mean if a graph has the same axis of symmetry as another?

• They are identical

• They are reflections

• They are symmetric about the same line

• They have the same roots