Quadratic Formula

The Quadratic Formula

Dr. Tom Giles

Quadratic Formula

Another way to solve quadratic equations.

This works for ALL quadratics (versus factoring that only works with rational solutions)

When to use the Quadratic Formula

Quadratic Formula

Types of Solutions

• Two Real Solutions ( no negatives under the radical)

• One Real Solution ( number under the radical simplifies to zero)

• No Real Solution

Multiple Choice

Which of the following quadratic equation is written in standard form?

• $$5x^2+4-3x=0$$

• $$12x=7x^2-8$$

• $$3x^2+5x=-13$$

• $$3x^2-8x+2=0$$

The Quadratic Formula

Multiple Choice

What is the value of -(-7)?

• -7

• -8

• 7

• 8

Multiple Choice

What is the value of (-3)^2?

• -6

• -9

• 6

• 9

Multiple Choice

Determine the values of a, b, and c for the quadratic equation:

4x² – 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

Fill in the Blanks

$3-5x^2=11x$  

In this quadratic, the  $a$   value is

?

Multiple Choice

Solve using the quadratic formula.
2x² - 9x - 35 = 0

• x = 7/2, x = -6
• x = -5/2, x =5
• x = -3/7, x =6
• x = -5/2, x = 7

Fill in the Blanks

$2x^2+x+7=5x^2-3$  

In this quadratic, the  $c$   value is

?

Multiple Choice

The quadratic equation can be used to solve quadratic equations that cannot be factored.

• True

• False

Fill in the Blanks

$-8x+4x^2-3=4x$  

In this quadratic, the  $b$   value is

?

Multiple Choice

Solve using the Quadratic Formula:

x² + 4x + 3 = 0

• x = 1 and x = 3

• x = 6 and x = -2

• x = -1 and x = -3

Using the Quadratic Formula

Multiple Choice

Use the quadratic formula to find the solutions for

y = -x² - 5x + 12

• No Real Solution

Fill in the Blanks

Set the following quadratic $=0$ to use the quadratic formula.

$-9p^2+6p+11=-4p$  

Identify the  $a$  ,  $b$  , and  $c$  values.  Write them in order with commas between.

Don't forget!!!

Fill in the Blanks

What are the two solutions for the expression below? 


$-3\pm5$  

List with a comma between the two solutions

Multiple Choice

What are the solutions of $$a^2=6a+3$$ ?

• $$a=\frac{7\pm\sqrt{129}}{2}$$  
  

• $$a=3\pm2\sqrt{3}$$  
  

• $$a=\frac{7\pm\sqrt{69}}{2}$$  
  

• $$a=\frac{-7\pm\sqrt{129}}{2}$$  
  

Multiple Choice

What are the solutions of $$-4b^2-12b=-6b^2+9-6b$$ ?

• $$b=3\pm3\sqrt{2}$$  

• $$b=\frac{-5\pm2\sqrt{7}}{3}$$  

• $$b=\frac{3\pm3\sqrt{3}}{2}$$  

• $$b=\frac{6\pm3\sqrt{11}}{7}$$  

Multiple Choice

What are the solutions of $$-1=-2x^2+3x$$ ?

• $$x=\frac{3\pm\sqrt{17}}{4}$$  

• $$x=\frac{-3\pm\sqrt{18}}{4}$$  

• $$x=\frac{3\pm\sqrt{17}}{-4}$$  

• $$x=\frac{3\pm\sqrt{18}}{2}$$  

Time to practice!!

Make sure you write the formula down in your notes

so you can complete the next 3 slides.