Algebra 1-Unit 3B Common Assessment: Solving Quadratics

When the expressions  $x^2-9$  and  $x^2-5x+6$   are factored, a common factor is which expression below?

• x - 2

• x - 3

• x + 3

• x squared

 Which of the following is equivalent to the expression below?
 $9x^2\ -\ 16$  

•  $\left(3x-4\right)^2$  

•  $\left(9x-4\right)\left(9x+4\right)$  

•  $\left(3x-8\right)\left(3x+8\right)$  

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

An expression is shown:  $81x^{4\ }-1$   . Jake rewrites the expression as a difference of squares so he can factor it. Which option shows how Jake could rewrite the expression?

•  $\left(9x^2\right)-1^2$  

•  $\left(9x^2\right)^2\ -1^2$  

•  $\left(9x\right)^{4\ }-1^2$  

•  $\left(9x\right)^{4\ }-1^4$  

On a windy morning, a hot air balloon starts rising and flying away from the top of a hill. The altitude, h, in feet, of the balloon x hours after starting its ascent from the hill, can be modeled by the function h(x) =  $-16x^2\ +64x+80$  
What is the y-intercept for this function? 

• -16

• 64

• 16

• 80

Solve by factoring.
 $x^2-8x-9\ =\ 0$  

•  $\left(x-9\right)\left(x+1\right)$  

•  $\left(x-9\right)^2$  

•  $\left(x\ +9\right)\left(x-1\right)$  

•  $\left(x+1\right)^2$  

Tags

CCSS.HSA.REI.B.4

CCSS.HSA.SSE.A.2

Solve by factoring.
 $x^2-10\ =\ 9x$  

•  $\left(x\ +\ 10\right)^2$  

•  $\left(x-10\right)^2$  

•  $\left(x+1\ \right)\left(x-10\right)$  

•  $\left(x\ -1\right)\left(x\ +\ 10\right)$  

Tags

CCSS.HSA.REI.B.4

CCSS.HSA.SSE.A.2

Solve by factoring.
 $2x^2\ +\ 10x\ +\ 8\ =\ 0$  

•  $\left(x-1\right)\left(x-4\right)$  

•  $\left(x+1\right)\left(x-4\right)$  

•  $\left(x\ +1\right)\left(x+4\right)$  

•  $\left(x-1\right)\left(x+4\right)$  

 $x^2\ +\ 7\ =\ 88$ 



 Solve by square roots.

•  $\pm9$  

•  $\pm81$  

•  $\pm5$  

•  $\pm10$  

 $6x^2\ =\ 54$  

Solve by square roots.

•  $\pm9$  

•  $\pm6$  

•  $\pm3$  

•  $\pm10$  

 $2x^2\ +\ 7x\ +\ 3\ =\ 12$  

Solve by using the quadratic formula.

•  $\lceil-\frac{1}{2\ },\ -3\rceil$  

•  $\lceil-2,\ -3\rceil$  

•  $\lceil-6,\ \frac{3}{4}\rceil$  

•  $\frac{\lceil1}{2},\ 3\rceil$