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)  $x^2-2x+\ ?\ =\ 2\ =\ 2+?$  

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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:

•  $ax^2+c=0$  

•  $ax^2+bx+c=0$  

•  $ax^2+bx=c$  

•  $ax^2+bx=0$  

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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.

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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?

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

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 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

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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

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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.

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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.

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