Unit 2 Study Guide Quadratics

What steps transform the graph of

 $y=x^2$  to  $y=-\left(x+2\right)^2+5$  ?

• translate 2 units to the right, translate down 5 units

• reflect across the x-axis, translate 2 units to the left, translate up 5 units

• reflect across the x-axis, translate 2 units to the right, translate down 5 units

• translate 2 units to the left, translate up 5 units

What steps transform the graph of $y=x^2$  to  $y=3\left(x-3\right)^2-4$  ?

• reflect across the x-axis, translate 3 units to the left, translate up 4 units, stretch by the factor 3

• translate 3 units to the right, translate down 4 units, stretch y the factor 3

• translate 3 units to the left, translate up 4 units, stretch by the factor 4

• reflect across the x-axis, translate 3 units to the right, translate down 4 units, stretch by a factor of 3

Use the vertex for to write the equation of the parabola.

• $y=-3\left(x+2\right)^2+2$

• $y=-3\left(x+2\right)^2-2$
  

• $y=-3\left(x-2\right)^2-2$
  

• $y=\left(x-2\right)^2-2$
  

What is the vertex for of the equation? $y=x^2+2x-6$  

•  $y=\left(x+1\right)^2+7$  
  

•  $y=\left(x+1\right)^2-7$  
  

•  $y=\left(x-1\right)^2+7$  
  

•  $y=\left(x-1\right)^2-7$  
  

Use the vertex form to write the equation of the parabola.

• $y=3\left(x-3\right)^2-2$

• $y=3\left(x-3\right)^2+2$
  

• $y=3\left(x+3\right)^2-2$
  

• $y=\left(x+3\right)^2-2$
  

What is the maximum or minimum value of the function?

 $y=2x^2+32x-8$  

• minimum value: -8

• minimum value: 8

• minimum value: -136

• minimum value: 136

Which of the quadratic functions below have the highest maximum value?

• Function A

• Function B

• Function C

• Function B and C have the same max

Identify the domain and range of the graph of the function

 $y=3\left(x+2\right)^2-2$  

• domain: all real numbers

  
  range: $y\le2$  

• domain:  $x\le-2$  

  
  

  range: all real numbers
  

• domain: all real numbers
  

  
  range:  $y\ge-2$  
  

• domain: all real numbers
  

  
  range: all real numbers
  
  

Identify the vertex and axis of symmetry of the graph of the function

 $y=-\left(x-3\right)^2+2$  

• vertex: (3,2)

  
  axis of symmetry: x=3

• vertex: (-3,2)

  
  

  axis of symmetry: x=-3
  

• vertex: (-3,-2)

  
  

  axis of symmetry: x=-3
  

• vertex: (3,-2)

  
  

  axis of symmetry: x=3
  

What is the average rate of change over the interval (-1 , 1).

• 4

• -4

• 2

• 8

• -8