Vertex and Intercepts of Quadratic Functions

The video tutorial explains how to convert a quadratic function from general form to vertex form. It begins by identifying the coefficients a, b, and c, and then calculates the axis of symmetry to find the x-coordinate of the vertex. The y-coordinate is determined by evaluating the function at this x-value. With the vertex coordinates and the value of a, the quadratic function is rewritten in vertex form. The tutorial concludes with a graphical verification of the results, highlighting the vertex and vertical intercept.

What is the first step in converting a quadratic function from general form to vertex form?

• Determine the axis of symmetry

• Identify the coefficients a, b, and c

• Find the y-intercept

• Graph the function

How do you calculate the axis of symmetry for a quadratic function?

• x = a / b

• x = c / a

• x = -b / 2a

• x = b / 2a

What is the x-coordinate of the vertex for the given quadratic function?

• 5/2

• 2.5

• 10

• 5

To find the y-coordinate of the vertex, what should you do?

• Find the derivative

• Set the function equal to zero

• Evaluate the function at x = 5/2

• Evaluate the function at x = 0

What is the y-coordinate of the vertex for the quadratic function?

• 50/4

• 33/4

• 25/4

• 8/4

What is the vertex form of the quadratic function given a = -1, h = 5/2, and k = 33/4?

• f(x) = (x + 5/2)^2 - 33/4

• f(x) = -(x + 5/2)^2 + 33/4

• f(x) = (x - 5/2)^2 - 33/4

• f(x) = -(x - 5/2)^2 + 33/4

Tags

CCSS.HSF-IF.C.7A

What does the graph of the quadratic function look like when a is negative?

• It opens upwards

• It opens downwards

• It is a straight line

• It is a circle

Tags

CCSS.HSF-IF.C.7A

What does the constant term c represent in the graph of a quadratic function?

• The vertex

• The y-intercept

• The x-intercept

• The slope of the graph

Where does the graph intersect the vertical axis?

• (0, 5)

• (2, 0)

• (5, 0)

• (0, 2)

How do you determine the vertical intercept of a quadratic function?

• Solve for the vertex

• Set y equal to zero

• Find the derivative

• Set x equal to zero