Graphing Quadratic Functions in Vertex Form

This lesson covers graphing quadratic functions in vertex form. It explains how to identify the vertex, axis of symmetry, and transformations. The video provides a step-by-step guide to graphing, including plotting the vertex, drawing the axis of symmetry, and finding additional points. A practice problem is solved to illustrate these steps. The lesson also demonstrates converting between vertex and standard forms of quadratic functions.

What is the vertex form of a quadratic function?

• f(x) = a(x + h)^2 + k

• f(x) = a(x - h)^2 + k

• f(x) = a(x - h)^2 - k

• f(x) = ax^2 + bx + c

If the vertex form of a quadratic function is f(x) = a(x + 2)^2 + 3, what is the vertex?

• (2, 3)

• (-2, 3)

• (2, -3)

• (-2, -3)

What is the axis of symmetry for the function f(x) = a(x - 4)^2 + 5?

• y = 4

• x = -4

• x = 4

• y = -4

Why can't the coefficient 'a' be zero in the vertex form of a quadratic function?

• It would make the function linear

• It would make the function cubic

• It would make the function constant

• It would make the function undefined

What is the first step in graphing a quadratic function in vertex form?

• Draw the axis of symmetry

• Evaluate the function for two additional points

• Draw a smooth curve through the points

• Identify and plot the vertex

Tags

CCSS.HSF-IF.C.7A

In the practice problem, what are the coordinates of the vertex for the function f(x) = 2(x - 3)^2 + 1?

• (3, -1)

• (3, 1)

• (-3, 1)

• (-3, -1)

How is the function f(x) = 2(x - 3)^2 + 1 transformed compared to the parent function?

• 3 units right, 1 unit down, vertically compressed by 2

• 3 units left, 1 unit up, vertically compressed by 2

• 3 units right, 1 unit up, vertically stretched by 2

• 3 units left, 1 unit down, vertically stretched by 2

What is the vertex of the function f(x) = 3(x + 2)^2 - 1?

• (2, -1)

• (-2, 1)

• (-2, -1)

• (2, 1)

What is the standard form of the function f(x) = 3(x + 2)^2 - 1?

• 3x^2 + 12x + 11

• 3x^2 + 12x - 1

• 3x^2 - 12x + 11

• 3x^2 - 12x - 1

How do you find the axis of symmetry for a quadratic function in standard form?

• x = a / 2b

• x = b / 2a

• x = -b / 2a

• x = -a / 2b