Graphing Quadratic Functions: Key Concepts and Techniques

This video tutorial covers graphing quadratic functions algebraically, focusing on identifying coefficients and properties such as the y-intercept, axis of symmetry, and vertex. It explains how to determine if the graph opens upward or downward based on the leading coefficient and demonstrates graphing steps for both positive and negative coefficients. The video concludes with contact information for further questions.

What is the standard form of a quadratic function?

• f(x) = ax^2 + bx^2 + c

• f(x) = ax^3 + bx + c

• f(x) = ax^2 + bx + c

• f(x) = ax + bx + c

In the function f(x) = 4x^2 - 8x + 3, what is the value of the coefficient 'a'?

• 1

• -8

• 4

• 3

How can you determine if the graph of a quadratic function opens upward or downward?

• By the value of 'b'

• By the value of 'c'

• By the sign of 'a'

• By the value of 'x'

What is the y-intercept of the function f(x) = 4x^2 - 8x + 3?

• (0, 3)

• (0, -8)

• (0, 4)

• (0, 1)

What is the formula for finding the axis of symmetry in a quadratic function?

• x = -b / 2a

• x = -b / a

• x = b / a

• x = b / 2a

For the function f(x) = 4x^2 - 8x + 3, what is the axis of symmetry?

• x = 1

• x = -1

• x = -2

• x = 2

What are the coordinates of the vertex for the function f(x) = 4x^2 - 8x + 3?

• (-1, -1)

• (-1, 1)

• (1, -1)

• (1, 1)

When graphing a quadratic function, what is the significance of the vertex?

• It is the highest or lowest point on the graph.

• It is where the graph intersects the y-axis.

• It is where the graph intersects the x-axis.

• It is the midpoint of the graph.

For the function f(x) = -x^2 - 2x + 1, what is the y-intercept?

• (0, -2)

• (0, -1)

• (0, 1)

• (0, 2)

What is the vertex of the function f(x) = -x^2 - 2x + 1?

• (-1, 2)

• (1, -2)

• (-1, -2)

• (1, 2)