Quadratic Functions and Their Properties

The video tutorial explains the effects of coefficients 'a', 'b', and 'c' on the shape of quadratic graphs. It begins with an introduction to the standard quadratic form ax^2 + bx + c. The tutorial then details how 'a' affects the graph's steepness and direction, 'c' shifts the graph vertically, and 'b' influences the slope at the y-intercept. By combining these effects, viewers learn to analyze and predict the shape of quadratic graphs.

What is the standard form of a quadratic equation?

• ax^2 + bx^2 + c

• ax^3 + bx^2 + c

• ax^2 + bx + c

• ax + b

What happens to the graph of y = ax^2 when 'a' is increased?

• The graph shifts to the left.

• The graph becomes steeper.

• The graph shifts to the right.

• The graph becomes wider.

If 'a' is negative, how does the graph of y = ax^2 behave?

• It becomes a circle.

• It opens downwards.

• It becomes a straight line.

• It opens upwards.

What is the effect of increasing 'a' on the graph's steepness?

• The graph shifts to the left.

• The graph shifts to the right.

• The graph becomes steeper.

• The graph becomes flatter.

What is the effect of the coefficient 'c' on the graph of a quadratic equation?

• It changes the slope.

• It changes the curvature.

• It shifts the graph horizontally.

• It shifts the graph vertically.

What is the y-intercept of a quadratic equation in the form ax^2 + bx + c?

• a

• 0

• b

• c

How does the graph of a quadratic equation change if 'c' is negative?

• The graph becomes steeper.

• The graph becomes wider.

• The graph shifts upwards.

• The graph shifts downwards.

If 'c' is increased, what happens to the graph?

• It shifts upwards.

• It shifts downwards.

• It becomes steeper.

• It becomes a straight line.

In a quadratic equation, what does a negative 'c' value indicate about the y-intercept?

• The y-intercept is positive.

• The y-intercept is zero.

• The y-intercept is negative.

• The y-intercept is undefined.

What role does the coefficient 'b' play in a quadratic equation?

• It determines the y-intercept.

• It affects the slope at the y-intercept.

• It alters the curvature of the graph.

• It changes the direction of the graph.