P4-C1-D1 Solving Quadratics Methods Comparison

Marleni starts to solve a quadratic by using the completing the square method.  The following show the first three steps of her work.  What number value is she missing in the third step?

 $2x^2-4x-4=0$  
1)  $2x^2-4x=4$  

2)  $x^2-2x=2$  

3)  $x^2-2x+\ ?\ =\ 2\ =\ 2+?$  

Osman was the solving the following equation:  $x^2-20x-28=-2$  
His first step in completing the square is to set up the equation in the following form:

•  $ax^2+c=0$  

•  $ax^2+bx+c=0$  

•  $ax^2+bx=c$  

•  $ax^2+bx=0$  

Lauren visited Marisa's home. She noticed this picture in her Remote Learning Scrapbook. What is this?

• This is the speed of light formula.

• This is the quadratic formula.

• This is the zero product property.

• This is scary.

Dymond is using the Quadratic Formula to solve this equation:  $x^2+8x-4=10x+1$  
First she decides to identify her a, b, and c values. What is the b value of this equation?

Takoya decides to solve  $x^2=-5x-6$ by factoring, what factors will she find? 

 Slyvester is solving a quadratic equation using the quadratic formula.  He reaches this step in the process:
 $x=\frac{-1\pm\sqrt{-35}}{6}$  
What should Sylvester's next step be?

• Stop solving and write "no solution" as his answer.

• Simplify the numerator by simplifying the radical

• Factor out a negative one from the numerator to continue simplifying

• No further steps are needed.  This is the final answer.

Jessua chooses to factor the following quadratic in order to solve: $x^2-14x+49=0$  
He gets  $\left(x-7\right)^2=0$  
What does this step tell Jessua about the number of x-intercepts that this quadratic has?

• One

• Two
  

• Zero

Yadiel, Elijah, and Jonathan were making a video on Completing the Square. What is their first step to solving this equation?

a² + 10a + 21 = 0

• Set the equation equal to zero

• Divide 10 by 2 and add the result to both sides

• Add a² and 10a together

• Subtract the 21

Lised tells Jazmin that solving a quadratic by the Completing the Square method will give you the same solutions as when you solve the same problem using the Quadratic Formula. Is she correct?

• No, Lised is not correct because only Factoring and Completing the Square result in the same solution.

• Yes, Lised is correct because all methods of solving quadratics result in the same solutions.

• Yes, Lised is correct is because Completing the Square and the Quadratic Formula result in the same solution.

• No, Lised is not correct because the three methods of solving quadratics will result in three different solutions.

Tarae, Charlotte, and Odaluis decide to work on the same quadratic equation using three different methods: solving by factoring, completing the square, and solving by the Quadratic Formula. What will the result be?

• They will get the same solutions from the factoring and completing the square, but a different solution when using the Quadratic Formula.

• All three solutions will be different.

• All three solutions will be the same.

• They will get the same solutions from using the Quadratic Formula and Completing the Square, but a different answer from solving by factoring.