3.3 Quadratic Formula

3.3 Quadratic Formula

When to use the Quadratic Formula

--> The formula comes in handy when the equation is written in standard form: $f\left(x\right)=ax^2+bx+c$   

but cannot be factored!

Notice: The formula is set equal to x, therefore we are solving for x-intercepts (zeros, roots of the equation).

Types of Solutions

• two real solutions ( no negatives under the radical)

• one real solution ( number under the radical simplifies to zero)

• two imaginary solutions ( negative under the radical

Lets solve using the Quadratic Formula! $x^2+3x-5=0$  

• Step 1: Make sure the equation is written in standard form (one side = 0)

• Step 2: Identify a, b and c in the equation

• Step 3: Plug the numbers into the quadratic formula!

• ​​  $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$  

• Step 4: Perform the operations and solve! 

Jump back to google classroom to follow along and solve the formula!

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

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

Multiple Choice

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

• True

• False

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

Multiple Choice

Use the quadratic formula to find the solutions for

y = -x² - 5x + 12

• No Real Solution