Understanding Quadratic Functions

This video tutorial by Mr. Backwork covers quadratic functions, focusing on their unique characteristics compared to linear functions. It explains the concept of parabolas, highlighting key features like the vertex and axis of symmetry. The tutorial includes step-by-step graphing of quadratic equations such as y = x^2, y = 3x^2, and y = -x^2 + 2, emphasizing the importance of correctly using parentheses when dealing with negative numbers in calculations. The video concludes with a demonstration of how the negative sign affects the parabola's orientation.

What distinguishes a quadratic function from a linear function?

• It has an x term.

• It has an x squared term.

• It has a constant term.

• It has a y-intercept.

What is the vertex of a parabola?

• The point where the parabola intersects the x-axis.

• The midpoint of the parabola.

• The point where the parabola intersects the y-axis.

• The highest or lowest point on the parabola.

How is the axis of symmetry of a parabola defined?

• A line parallel to the x-axis.

• A diagonal line through the vertex.

• A vertical line through the vertex.

• A horizontal line through the vertex.

What is the vertex of the parabola y = x^2?

• (0, 0)

• (1, 1)

• (-1, -1)

• (2, 4)

Why is it important to use parentheses when squaring negative numbers?

• To ensure the result is negative.

• To ensure the result is positive.

• To avoid calculator errors.

• To simplify the equation.

What happens to the graph of y = 3x^2 compared to y = x^2?

• It shifts upwards.

• It shifts downwards.

• It becomes narrower.

• It becomes wider.

What is the vertex of the parabola y = 3x^2?

• (2, 12)

• (0, 0)

• (-1, 3)

• (1, 3)

How does a negative coefficient affect the orientation of a parabola?

• It opens to the left.

• It opens to the right.

• It opens upwards.

• It opens downwards.

What is the vertex of the parabola y = -x^2 + 2?

• (2, 0)

• (-1, 1)

• (1, 1)

• (0, 2)

What is the axis of symmetry for the parabola y = -x^2 + 2?

• x = 2

• x = -1

• x = 1

• x = 0