Exploring Quadratic Characteristics

The video tutorial covers the characteristics of quadratic functions, explaining their standard form and the graph known as a parabola. It discusses the symmetry of the graph, the axis of symmetry, and the vertex. The tutorial includes exercises analyzing different quadratic functions, focusing on finding the axis of symmetry and vertex by plotting points and using formulas.

Which of the following is the general form of a quadratic function?

• f(x) = a/x + b

• f(x) = ax^3 + bx^2 + c

• f(x) = ax^2 + bx + c

• f(x) = ax + b

What is the graph of a quadratic function called?

• Ellipse

• Parabola

• Circle

• Line

What is the simplest quadratic function?

• f(x) = x^3

• f(x) = x^2

• f(x) = x

• f(x) = 1/x

The graph of the squaring function is symmetric to which axis?

• None

• z-axis

• y-axis

• x-axis

What is the axis of symmetry for the function f(x) = x^2?

• x = 2

• x = 1

• x = -1

• x = 0

For the function f(x) = x^2 + 4x + 3, what is the axis of symmetry?

• x = -1

• x = 1

• x = 2

• x = -2

For the function f(x) = x^2 + 4x + 3, what is the vertex?

• (-2, 1)

• (2, 1)

• (2, -1)

• (-2, -1)

For the function g(x) = x^2 - 4x, what is the axis of symmetry?

• x = -2

• x = 2

• x = -1

• x = 1

For the function g(x) = x^2 - 4x, what is the vertex?

• (2, 4)

• (-2, -4)

• (-2, 4)

• (2, -4)

For the function h(x) = -x^2 + 4x, what is the vertex?

• (2, -4)

• (2, 4)

• (-2, 4)

• (-2, -4)