Graphing Quadratic Functions: Forms and Features

This video tutorial covers the basics of graphing parabolas, including understanding the vertex, axis of symmetry, and the effects of coefficients on the shape of the parabola. It explains how to graph parabolas in standard, vertex, and intercept forms, and discusses the domain and range. The tutorial provides step-by-step instructions and examples to help learners grasp these concepts effectively.

What is the vertex of a parabola?

• The point where the parabola intersects the axis of symmetry

• The highest or lowest point on the parabola

• The point where the parabola crosses the y-axis

• The point where the parabola crosses the x-axis

What does the axis of symmetry do?

• Splits the parabola into two equal halves

• Determines the width of the parabola

• Indicates the direction the parabola opens

• Shows the range of the parabola

What is the domain of any parabola?

• All positive numbers

• All integers

• All real numbers

• All negative numbers

How does the coefficient of x² affect the shape of the parabola?

• It alters the axis of symmetry

• It changes the vertex of the parabola

• It affects the width of the parabola

• It determines the direction the parabola opens

In standard form, what is the formula to find the axis of symmetry?

• x = -b/2a

• x = a/2b

• x = b/2a

• x = -a/2b

What does the 'c' in the standard form equation y = ax² + bx + c represent?

• The x-intercept

• The y-intercept

• The vertex

• The axis of symmetry

In vertex form, what do the h and k represent in the equation y = a(x - h)² + k?

• The coefficients of the parabola

• The x and y intercepts

• The axis of symmetry and range

• The vertex coordinates

How do you determine the vertex in vertex form?

• By finding the axis of symmetry

• By solving for x and y intercepts

• By using the coefficients a and b

• By taking the opposite sign of h and using k

In intercept form, what do the values p and q represent in the equation y = a(x - p)(x - q)?

• The axis of symmetry

• The y-intercepts

• The x-intercepts

• The vertex coordinates

How do you find the axis of symmetry in intercept form?

• By finding the midpoint between p and q

• By solving for the vertex

• By using the formula x = -b/2a

• By using the value of c