Understanding Quadratic Functions

This video tutorial covers graphing quadratic functions in general form, focusing on parabolas. It explains the properties of parabolas, including the vertex, axis of symmetry, and intercepts. The tutorial provides two examples: graphing f(x) = x^2 - 4 and f(x) = -x^2 + x + 6, demonstrating how to find the vertex, axis of symmetry, and intercepts for each. The video emphasizes understanding the general form of quadratic functions and how the sign of 'a' affects the parabola's direction.

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

• Intercept

• Axis

• Vertex

• Focus

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

• Tangent

• Chord

• Directrix

• Axis of symmetry

In the general form of a quadratic function, what does the sign of 'a' determine?

• The width of the parabola

• The position of the vertex

• The direction the parabola opens

• The number of intercepts

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

• (0, 4)

• (-4, 0)

• (0, -4)

• (4, 0)

How do you find the x-intercepts of a quadratic function?

• Set f(x) to zero and solve for x

• Set x to zero and solve for f(x)

• Find the vertex

• Use the axis of symmetry

In the function f(x) = -x^2 + x + 6, what is the axis of symmetry?

• x = 1

• x = -1/2

• x = 1/2

• x = -1

What is the vertex of the function f(x) = -x^2 + x + 6?

• (0, 6)

• (1/2, 25/4)

• (1, 6)

• (1/2, 6.25)

For the function f(x) = -x^2 + x + 6, what are the x-intercepts?

• (-2, 0) and (3, 0)

• (2, 0) and (-3, 0)

• (3, 0) and (-2, 0)

• (0, -2) and (0, 3)

What is the y-intercept of the function f(x) = -x^2 + x + 6?

• (0, -6)

• (6, 0)

• (0, 6)

• (-6, 0)

What is a good way to verify the correctness of a parabola's graph?

• Count the intercepts

• Measure the width

• Ensure symmetry about the axis

• Check the vertex