Algebra II Topic 5 Test

Graph the function. How is the graph a translation of $f\left(x\right)=x^2$ ?:

 $y=\left(x-1\right)^2+3$  

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Identify the vertex and the axis of symmetry of the graph of the function  $y=-2\left(x+3\right)^2+5$ .

• vertex:  $(–3,–5)$ ;
  axis of symmetry:  $x=-3$  

• vertex:  $\left(3,5\right)$ ;axis of symmetry:  $x=3$  

• vertex:  $\left(3,-5\right)$ ;axis of symmetry:  $x=3$  

• vertex:  $\left(-3,5\right)$ ;axis of symmetry:  $x=-3$  

Identify the maximum or minimum value and the domain and range of the graph of the function   $y=3\left(x-3\right)^2-3$ .

• minimum value:     $3$  
  domain: all real numbers  $\ge3$  
  range: all real numbers  

• maximum value:     $-3$  
  domain: all real numbers  $\le-3$  
  range: all real numbers

• maximum value:     $3$  
  domain: all real numbers 
  range: all real numbers  $\le3$  

• minimum value:     $-3$  
  domain: all real numbers
  range: all real numbers  $\ge-3$  

What steps transform the graph of $y=x^2$  to  $y=-2\left(x-3\right)^2+5$ ?

• reflect across the x-axis, translate 3 units to the right, translate up 5units, stretch by the factor 2

• translate 3 units to the right, translate up 5 units, stretch by the factor 2  

•  reflect across the x-axis, translate 3 units to the left, translate down 5 units, stretch by the factor 2

• translate 3 units to the left, translate down 5 units, stretch by the factor 2 

• $y=\left(x+3\right)^2-2$

• $y=-\left(x-3\right)^2+2$

• $y=-\left(x+3\right)^2-2$

• $y=-\left(x-3\right)^2-2$

What are the vertex and the axis of symmetry of the equation?

 $y=-2x^2+8x-20$  

• Vertex:       $\left(-2,12\right)$  
  Axis of Symmetry:      $y=-2$  

• Vertex:       $\left(2,-12\right)$ 
  Axis of Symmetry:      $x=2$  

• Vertex:       $\left(-2,-12\right)$ 
  Axis of Symmetry:      $x=-2$  

• Vertex:       $\left(2,-12\right)$ 
  Axis of Symmetry:      $x=-12$  

What is the maximum or minimum value of the function? What is the range? 

 $y=2x^2+28x-8$  

• Minimum Value:      $7$  
  Range:       $y\ge7$  

• Minimum Value:      $-7$  
  Range:       $y\ge-7$  

• Minimum Value:   $-106$  
  Range:          $y\ge-106$  

• Minimum Value:      $-106$  
  Range:       $y\ge-7$  

What is the graph of the equation?

 $y=-x^2+2x+3$  

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What is the vertex form of the equation?

 $y=-x^2+2x-8$  

•  $y=\left(x-1\right)^2+7$  

•  $y=-\left(x-1\right)^2-7$  

•  $y=-\left(x+1\right)^2+7$   

•  $y=\left(x+1\right)^2-7$  

Sketch a parabola with an axis of symmetry $x=-1$  , y-intercept $\left(0,1\right)$   , and point  $\left(1,-5\right)$ . 

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