Best Method for Solving Quadratics

Best Method for Solving Quadratics

by Kellen Laws

​Methods for Solving Quadratics

• ​Factoring

• ​Isolation/Using Square Roots

• ​Completing the Square

• ​Quadratic Formula

Poll

Which method are the MOST confident in using?

• Solving Quadratics by Factoring

• Solving Quadratics by Isolation/Using Square Roots

• Solving Quadratics by Completing the Square

• Solving Quadratics by Quadratic Formula

Poll

Which method are the LEAST confident in using?

• Solving Quadratics by Factoring

• Solving Quadratics by Isolation/Using Square Roots

• Solving Quadratics by Completing the Square

• Solving Quadratics by Quadratic Formula

Multiple Choice

Which option shows what quadratics in standard form look like?

• $$ax+bx^2+c$$  

• $$a+bx+cx^2$$  

• $$ax^2+bx+c$$  

• $$ax^2+b+cx$$  

​When to use Zero Product Property/Factoring...

Multiple Choice

Use Factoring and the Zero Product Property to solve:

$$0=x^2+2x-15$$  

• x = 5

  and

  x = 3

• x = -5

  and

  x=-3

• x = 5

  and

  x = -3

• x = -5

  and

  x = 3

​COMPLETING THE SQUARE

​Remember: f(x) = ax² + bx + c

​

Use when "a" is equal to 1.

​

​Use when "b" is an even number

Multiple Choice

What should be added to both sides of the following equation to COMPLETE THE SQUARE?

$$x^2+12x=5$$  

• $$-\left(\frac{12}{2}\right)^2\ or\ -36$$  

• $$\left(\frac{12}{2}\right)^2\ or\ 36$$  

• $$\left(\frac{5}{2}\right)^2\ or\ \frac{25}{4}$$  

• $$\left(\frac{12}{2}\right)\ or\ 6$$  

Multiple Choice

What will the perfect square BINOMIAL look like from the equation

$$x^2+12x=5$$  

• $$\left(x-6\right)^2=5-36$$  

• $$\left(x+12\right)^2=5+144$$  

• $$\left(x-6\right)^2=5+36$$  

• $$\left(x+6\right)^2=5+36$$  

​Isolation or Solving w/Square Roots

• ​Will have the form of:

• ​ax² + c = 0 or ax² = c

• ​a(x + #)² = #

• ​

• ​Remember you are ISOLATING the variable!!

Multiple Choice

Solve the following by ISOLATION

$$4\left(x-5\right)^2=12$$  

• $$\left(4x+20\right)^2=12$$  

• $$x=5\pm\sqrt[]{3}$$  

• $$x=-5\pm\sqrt[]{3}$$  

• $$x=5\pm\frac{1}{2}\sqrt[]{3}$$  

Quadratic Formula​

Multiple Choice

Of the following Quadratic...what are the a, b, & c values of the given function?

$$4x^2-8x=3$$  

• a = 4

  b = 8

  c = 3

• a = 4

  b = -8

  c = -3

• a = 4

  b = -8

  c = 3

• a = 4

  b = 8

  c = -3

Poll

Which method do you feel is the best way to solve the following?

$$x^2-3x-54=0$$  

• Factor

• Isolation/Solve with Square Roots

• Complete the Square

• Quadratic Formula

Poll

Which is option do you feel is the best to solve the following function?

$$x^2+2x=-9$$  

• Factor

• Isolation/Solve with Square Roots

• Complete the Square

• Quadratic Formula

Poll

Which option do you believe is the best to solve the following?

$$4\left(x+2\right)^2=8$$  

• Factor

• Isolation/Solve with Square Roots

• Complete the Square

• Quadratic Formula

Poll

Which option do you feel is the best possible for the following function?

$$3x^2+13x+4=0$$  

• Factor

• Isolation/Solve with Square Roots

• Complete the Square

• Quadratic Formula

Poll

Which option do you believe is the best option for the following function?

$$3x^2+13x+5=0$$  

• Factor

• Isolation/Solve with Square Roots

• Complete the Square

• Quadratic Formula