SAT: Quadratics

 $\left(2x+6\right)\ +\ \left(x^2+2x+1\right)$  

Which of the following polynomials is equivalent to the expression above?

(easy, no calculator)

•  $x^2+5$  

•  $x^2+7$  

•  $4x^2+7$  

•  $x^2+4x+7$  

 $x\left(x+2\right)=8$  
Which of the following lists all solutions to the quadratic equation above?

(easy, no calculator)

• 8 and 6

• 4 and -2

• -4 and 2

•  $\sqrt{6}$  

In the xy-plane, the graph of

 $y=\left(x-6\right)^2+3$  is the image of the graph of  $y=\left(x+5\right)^2+3$  after a translation of how many units to the right?  


(medium, calculator)

 $4a^2+20ab+25b^2$  

Which of the following is a factor of the polynomial above?

(medium, calculator)

•  $a+b$  

•  $2a+5b$  

•  $4a+5b$  

•  $4a+25b$  

Which of the following equivalent forms of the function  $f\left(x\right)=4x^2+4x-24$  is the most suitable to indicate the x-coordinate of the x-intercepts of the graph of  $y=f\left(x\right)$  in the xy-plane?

(medium, calculator) 

•  $f\left(x\right)=4\left(x^2+x-6\right)$  

•  $f\left(x\right)=4\left(x-2\right)\left(x+3\right)$  

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

•  $f\left(x\right)=\left(2x-4\right)\left(2x+6\right)$  

 $x^2-6x+11=y$  

 $x=y+1$  

The system of equations above is graphed in the xy-plane.  Which of the following is the y-coordinate of an intersection point (x,y) of the graphs of the two equations?

(medium, no calculator)

• -4

• -2

• 2

• 4

If  $4x^2+bx+9=0$  , where b is a constant, has exactly one solution, what is a possible value of b?

(medium, calculator)

• 72
  

• 36

• 12

• 6

 $\left(1-x\right)\left(x+2\right)^2\left(x+3\right)=0$  
Which of the following is a solution to the equation above?

(medium, calculator)

• -2

• -1

• 2

• 3

Of the following, which is the best model for the data in the scatterplot?

(medium, calculator)

• 
  

   $y=2x^2-11x-20$  
  

•  $y=2x^2-11x+20$  

•  $y=2x^2-5x-3$  

•  $y=2x^2-5x+3$  

Which expression is equivalent to  $\sqrt{16x^{16}}$  , where  $x>0$  ?

(hard, no calculator)

•  $4x^4$  

•  $4x^8$  

•  $8x^4$  

•  $8x^8$