Understanding Quadratic Functions and Their Properties

The video tutorial covers quadratic functions, focusing on their key features such as the axis of symmetry, vertex, and graph orientation. It explains how changes in the equation affect the graph's width and direction, and how to identify intervals of increase and decrease. The tutorial also demonstrates how to compare rates of change using the slope formula and applies quadratic functions to solve practical problems.

What is the general form of a quadratic function?

• f(x) = ax^2 + b

• f(x) = ax^3 + bx^2 + c

• f(x) = ax^2 + bx + c

• f(x) = ax + b

Why can't the coefficient 'a' in a quadratic function be zero?

• It would make the function undefined.

• It would turn the function into a linear equation.

• It would make the function a cubic equation.

• It would have no effect on the function.

What is the shape of the graph of a quadratic function called?

• Circle

• Parabola

• Hyperbola

• Ellipse

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

• x = 2

• x = 0

• x = -1

• x = 1

Where is the vertex of the parent function f(x) = x^2 located?

• (2, 2)

• (-1, -1)

• (0, 0)

• (1, 1)

What happens to the parabola when the coefficient 'a' is negative?

• It opens upwards.

• It opens downwards.

• It becomes a straight line.

• It becomes a circle.

If the absolute value of 'a' is greater than 1, what happens to the parabola?

• It becomes wider.

• It becomes a straight line.

• It becomes narrower.

• It remains unchanged.

In which interval does the function f(x) = 4x^2 increase?

• x = 0

• x < 1

• x > 0

• x < 0

For the function f(x) = -2.5x^2, in which interval does it decrease?

• x > 0

• x < 0

• x < 1

• x = 0

What is the formula for calculating the slope or rate of change?

• y1 - y2 / x1 - x2

• x1 - x2 / y1 - y2

• x2 - x1 / y2 - y1

• y2 - y1 / x2 - x1