Exploring Quadratic Functions and Their Graphs

This video introduces graphing quadratic functions, covering the standard, vertex, and factored forms. It explains the characteristics of parabolas, including the axis of symmetry and vertex. The video guides viewers through graphing quadratic functions, using example problems to illustrate the process. Key concepts such as domain, range, and the impact of the 'a' value on the graph's direction are discussed.

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

• f(x) = ax + b

• f(x) = a(x - m)(x - p)

• f(x) = a(x - h)^2 + k

• f(x) = ax^2 + bx + c

What is the shape of a quadratic function called?

• Parabola

• Hyperbola

• Circle

• Ellipse

What is the line called that cuts a parabola into two symmetrical halves?

• Central Line

• Median Line

• Line of Best Fit

• Axis of Symmetry

How many times does the axis of symmetry touch the parabola?

• Twice

• Three times

• Never

• Once

What is the highest or lowest point on a parabola called?

• Intercept

• Vertex

• Directrix

• Focus

What is the formula to calculate the axis of symmetry in standard form?

• x = -b/2c

• x = -b/2a

• x = -a/2b

• x = -c/2a

In the function f(x) = x^2, what are the values of a, b, and c?

• a = 0, b = 0, c = 1

• a = 0, b = 1, c = 0

• a = 1, b = 1, c = 1

• a = 1, b = 0, c = 0

If a quadratic function has a negative 'a' value, which way does the parabola open?

• To the right

• Downwards

• To the left

• Upwards

What is the domain of all quadratic functions?

• All integers

• All real numbers

• All negative real numbers

• All positive real numbers

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

• (0, 4)

• (4, 0)

• (0, 0)

• (-4, 0)