Vertex Form Review

Vertex Form Review

Mr. Mangano

Multiple Choice

Is function represented by the table linear or nonlinear?

• linear
• nonlinear

Multiple Choice

Is this function linear or nonlinear?

• Linear
• Nonlinear

​Recall The Quadratic Relation

​Linear Relationships have a constant first difference (a constant rate of change)

Qudratic Relations have a constant second difference

Multiple Choice

Which differences identify a function as linear?

• First Differences

• Second Differences

• Third Differences

• Fourth Differences

Multiple Choice

Which differences identify a quadratic function?

• First Differences

• Second Differences

• Third Differences

• Fourth Differences

Multiple Choice

True or False? The table represents a quadratic function.

• True

• False

​Degree of Polynomial

​The Highest Degree of a linear function (the number in the expoennt) is 1

​y=mx+b

​You can identify a quadratic expression (or second-degree expression) because it’s an expression that has a variable that’s squared and no variables with powers higher than 2 in any of the terms. (The degree is no higher than 2)

Multiple Choice

$$3m+8=15$$  

• Quadratic

• Not Quadratic

Multiple Choice

$$x^2-5x+10=0$$  

• Quadratic

• Not Quadratic

Multiple Choice

$$12-4x=10$$  

• Quadratic

• Not Quadratic

Multiple Choice

$$2t^2-7t=12$$  

• Quadratic

• Not Quadratic

The Parabola

When we graph a quadratic relation we see that it creates a special kind of curve known as the parabola

​

Multiple Choice

What is the vertex of this parabola?

• (0, 5)

• (2, 1)

• (-1, 2)

• (-2, 1)

Multiple Choice

The axis of symmetry line passes through which point?

• y-intercept
• any random point
• vertex
• symmetrical point for the vertex

​One particular form of a quadratic equation is vertex form

​It is useful because it tells you what the vertex of the parabola is without having to do any serious heavy lifting

​Vertex Form

Multiple Choice

What is the vertex of the equation

$$y=\left(x-3\right)^2+5$$  

• (-3, 5)

• (3, 5)

• (-3, -5)

• (3, -5)

Multiple Choice

What is the vertex of the equation

$$y=\left(x+7\right)^2+3$$  

• (7, 3)

• (7, -3)

• (-7, 3)

• (-7, -3)

Multiple Choice

What is the vertex of the equation

$$y=\left(x-4\right)^2$$  

• (-4, 0)

• (4, 0)

• (0, 4)

• (0, -4)

Multiple Choice

What is the vertex of the equation

$$y=x^2-1$$  

• (0, -1)

• (0, 1)

• (1, 0)

• (-1, 0)

Multiple Choice

What is the vertex of the equation

$$y=2\left(x+1\right)^2-5$$  

• (1, -5)

• (-1, -5)

• (-1, 5)

• (1, 5)

Multiple Choice

What is the vertex of the equation

$$y=-2\left(x-1\right)^2+5$$  

• (-1, -5)

• (-1, 5)

• (1, 5)

• (1, -5)

​Stretch / Compression Factor

​The 'a' vbalue of the vertex tells you how stretched or compressed yoru parabola will be

​If a is positive it opens up

​If a is negative it opens down

​The bigger the number of a the more stretched the parabola becomes

​The closer a gets to zero the more compressed the parabola becomes

​

Open Ended

Write the equation of a quadratic that is stretched by a factor of 6

Open Ended

Write the equation of a quadratic that is compressed by a factor of 1/3

​The Step Pattern

​The Step Pattern when a =1 is always 1,3,5

​Anytime you see a different number for a that is essentially the multipier for your step pattern

Open Ended

What is the step pattern for $$y=3x^2$$  

Open Ended

What is the step pattern for $$-2\left(x+5\right)^2-3$$  

​Graphing Parabolas

​When graphing parabolas given the vertex form simply mark your vertex and follow the step pattern starting at the vertex

​

If you are given the graph of a parabola identify the coordinates of the vertex and then identify the step pattern to find the 'a value'

Multiple Choice

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

• Maximum
• Minimum

Multiple Choice

What steps transform the graph y = x² to y = 2(x+2)² - 5?

• shrink by 2, shifted 2 units left and 5 down

• Stretch by 5, shifted 5 units left and 2 down

• Stretch by 2, shifted 2 units left and 5 down

• shrink by 5, shifted 2 units left and 2 down

Multiple Choice

What steps transform the graph y = x² to y = x² + 8

• shifted up 8 units

• shifted down 8 units

• shifted left 8 units

• shifted right 8 units

Multiple Choice

What steps transform the graph y = x² to y = (x-4)²

• Shifted down 4 units

• Shifted left 4 units

• Shifted right 4 units

• Shifted up 4 units

Multiple Choice

What is the equation of this graph?

• f(x) = (x -5)² + 1
• f(x) = (x - 1)² - 5
• f(x) = (x + 1)² - 5
• f(x) = (x + 5)² +1

Multiple Choice

Which of the following is the correct equation for the given graph?

• f(x) = (x - 2)² - 1
• f(x) = (x + 2)² - 1
• f(x) = -(x + 2)² - 1
• f(x) = -(x - 2)² - 1

Multiple Choice

What is the equation of this graph?

• f(x) = (x -5)² + 1
• f(x) = (x - 1)² - 5
• f(x) = (x + 1)² - 5
• f(x) = (x + 5)² +1