Section 4.1 - Quadratic Functions & Transformations - Graphing in Vertex Form

Section 4.1 - Quadratic Functions & Transformations - Graphing in Vertex Form

​Objective & Standard

• ​Identify and graph quadratic functions written in vertex form

MAFS.912.F-BF.2.3 - Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

Multiple Choice

Which of the following is a transformation of the graph y = x² + 4 ?

• Shifts left 4.

• Shifts right 4.

• Shifts up 4.

• Shifts down 4.

Multiple Choice

Which of the following is a transformation of the graph y = (x - 5)² ? 

• Shifts right 5.

• Shifts left 5.

• Shifts up 5.

• Shifts down 5.

Multiple Choice

Given: y = 2(x - 5) + 6, the vertex is

• (2, -5)

• (-5, 6)

• (2, 6)

• (5, 6)

Multiple Choice

Given the equation for this parabola:  y=-(x-4)²-3, does this parabola have a maximum or minimum value?

• Maximum

• Minimum

• Not enough information

Multiple Choice

What is the domain of the function y = x² + 3?

• All Real Numbers

• x>3

• x<3

• It is impossible to determine.

Multiple Choice

Find the range of the function   y = -2(x + 4)^2 + 7

• (-∞, -4]

• (-∞, 7]

• [7, ∞)

• [-4, ∞)

Multiple Choice

Which steps transform the graph of $$y=x^2$$   to $$y=2\left(x+2\right)^2-5$$ ? 

Multiple Choice

Which is the graph of $$y=2\left(x+2\right)^2-5$$ ? 

​Writing a Quadratic Function in Vertex Form

• Need the coordinates of the vertex

• ​Need the coordinates of a second point

• ​Substitute the vertex (h,k) and the point in the the vertex form equation to find the value of 'a'

• ​Write the function in vertex form.

Multiple Choice

What is the quadratic function for the graph shown?

• $$f\left(x\right)=-3\left(x+2\right)^2+6$$  

• $$f\left(x\right)=3\left(x-2\right)^2-6$$  

• $$f\left(x\right)=-3\left(x+2\right)^2-6$$  

• $$f\left(x\right)=3\left(x+2\right)^2-6$$  

• $$f\left(x\right)=3\left(x-6\right)^2-2$$