Understanding Quadratic Functions and Parabolas

The video tutorial explains how to analyze a quadratic function using a table of values. It covers identifying the vertex, axis of symmetry, and intercepts, and demonstrates how to graph the parabola. Finally, it shows how to write the equation of the parabola in factored form using the roots derived from the intercepts.

What is the vertex of a parabola if the smallest y-value in the table is -4?

• (-4, -3)

• (-3, -4)

• (3, 4)

• (4, 3)

What does the vertex of a parabola represent if it opens upwards?

• The midpoint of the graph.

• The lowest point on the graph.

• The point of inflection.

• The highest point on the graph.

How do you determine the axis of symmetry for a parabola?

• It is the y-coordinate of the vertex.

• It is the average of the y-intercepts.

• It is the x-coordinate of the vertex.

• It is the average of the x-intercepts.

What is the vertical intercept of a parabola if the x-value is 0?

• (-5, 0)

• (0, -5)

• (5, 0)

• (0, 5)

How are the points on a parabola related to the axis of symmetry?

• They are randomly placed.

• They are symmetrical across the axis of symmetry.

• They are only on one side of the axis.

• They are equidistant from the vertex.

What are the horizontal intercepts of a parabola if the y-value is 0?

• (0, 5) and (0, 1)

• (-5, 0) and (-1, 0)

• (5, 0) and (1, 0)

• (0, -5) and (0, -1)

What is the significance of the horizontal intercepts in a quadratic function?

• They are the maximum points.

• They are the points of inflection.

• They are the roots or zeros of the function.

• They are the minimum points.

What is the general form of a quadratic equation in factored form?

• y = a(x - r1)(x + r2)

• y = a(x + r1)(x + r2)

• y = a(x - r1)(x - r2)

• y = a(x + r1)(x - r2)

How do you find the value of 'a' in the factored form of a quadratic equation?

• By using the axis of symmetry.

• By using the horizontal intercepts.

• By using any point on the parabola except the intercepts.

• By using the vertex.

What is the final equation of the parabola if a = 1?

• y = (x - 5)(x - 1)

• y = (x + 5)(x + 1)

• y = (x - 5)(x + 1)

• y = (x + 5)(x - 1)