A2H The Quadratic Formula Lesson

Unit 5: Solving Quadratic Equations

The Quadratic Formula

Use this Quizizz lesson to practice solving quadratic equations with the quadratic formula. There is a video included of how to solve quadratic equations when complex/imaginary numbers are involved. He teaches it almost exactly how I would teach the lesson.

The Quadratic Formula:

If d > 0, there are 2 real solutions.

If d = 0, there is 1 real solution.

If d < 0, there are 2 imaginary solutions.

Meanings:

The discriminant is the part of the quadratic formula that is under the radical sign.

The Discriminant

​On the next slide: watch a video showing a quick review of how to use the quadratic formula to solve a quadratic equation with 2 real solutions.

Multiple Choice

Identify a, b and c in the quadratic equation: $$2x^2-3x-5=0$$  

• a = 2 , b = 3, c = -5

• a = 2, b = -3, c = 5

• a = 2, b = -3, c = -5

• a = -2, b = 3, c = 5

Multiple Choice

$$b^2-4ac$$  is called the . . .

• Square root

• Quadratic formula

• X-intercepts

• Discriminant 

Multiple Choice

Solutions of a quadratic equation are also called

• roots

• x-intercepts

• zeros

• All of the above

Multiple Choice

If there are no real solutions, the discriminant is

• zero

• a postive number

• a negative number

• a perfect square

Multiple Choice

If there is one solution, the discriminant is . . .

• zero

• a postive number

• a negative number

• a perfect square

Multiple Choice

Solve Using the Quadratic Formula
 x² + 4x - 40 = -8

• -10 & -4

• -4 & 10

• -8 & 4

• 8 & -4

Multiple Choice

Solve the following equation using the quadratic formula: $$3x^2+16x+5=0$$  

• $$x=\frac{1}{3},\ x=5$$  

• $$x=-\frac{1}{3},\ x=-5$$  

• $$x=-1,\ x=-15$$  

• $$x=1,\ x=15$$  

Multiple Choice

Solve the following equation using the quadratic formula: $$5x^2-6=13x$$  

• $$x=-2,\ x=-\frac{3}{5}$$  

• $$x=2,\ x=\frac{3}{5}$$  

• $$x=3,\ x=-\frac{2}{5}$$  

• undefined 

On the following slide...

Watch the following video to see an example of a quadratic equation with a complex/imaginary solution. Then, use the practice problems to build your skills.

Multiple Choice

What should you do first in solving this equation?

x² + 6x - 13 = 3

• Factor

• Write down: a = 1, b = 6, c = -13

• Subtract 3 from both sides.

• Add 3 to both sides.

Multiple Choice

What is the discriminate of f(x) = 3x² - 5x + 8
and how many solutions does the function have?

• discriminate = -71 and two imaginary solutions

• discriminate = -121 and has two imaginary solutions

• the discriminate = - 71 and has two real solutions

• the disctiminate = -121 and has two real solutions

Multiple Choice

Will the following equation have an IMAGINARY answer
11x²-9x+3=0

• yes

• no

Multiple Choice

Determine the value of the discriminant and name the nature of the solution for the following:

x² + 7x + 13

Remember: b² - 4ac

• 400 -:2 real, rational

• 0 :1 real, rational

• √(-400) -:2 non-real complex - imaginary

• -3 : 2 non-real , imaginary

Multiple Choice

Solve -2x² + 4x = 9

• (2 - i√14)/2   ,   (2 + i√14)/2

• (2 - i√-56)/2   ,   (2 + i√-56)/2

• (2 - i√-14)/2   ,   (2 + i√-14)/2

• (2 - √14)/2   ,   (2 + √14)/2

Multiple Choice

Solve using the quadratic formula.

$$r^2-2r+4=0$$  

• $$\left\{1\right\}$$  

• $$\left\{1+i\sqrt[]{3},\ 1-i\sqrt[]{3}\right\}$$  

• $$\left\{1.618,\ -0.618\right\}$$  

• $$\left\{\frac{1+i\sqrt[]{3}}{2},\ \frac{1-i\sqrt[]{3}}{2}\right\}$$