1. 9.4 the Quadratic Formula
Earlier we looked at how to solve quadratic equations in the form of ax2 + c = 0 by taking the square root.
We are going to look at how to solve ANY quadratic equation in standard form of ax2 + bx + c = 0
To do this, we use the QUADRATIC FORMULA. No one knows who discovered it, but versions of it go back as far as 2000 B.C. in Babylonia (4,000 yrs. ago)

2. QUADRATIC FORMULA. X = -b +- b2 – 4ac 2a
To use the quadratic formula, your equation must be in standard form.
Tells you what the x-intercepts of the equation are.
With a quadratic equation, you may have 2 x-intercepts, 1, or none. (see graphs)
X = -b +- b2 – 4ac 2a

3. Using the quadratic equation
Coefficient of x2 is the “a”, coefficient of x is the “b”, and what’s being added is the “c”
Solve using the quadratic formula
X2 + 5x – 14 = 0
X = 2 & -7

4. To graph a quadratic equation
Find the vertex
Use the quadratic formula to find the x-intercepts.
If there are no x-intercepts, choose an x-value to the right & to the left of the vertex & solve for y

5. graph
Find the vertex & use the quadratic formula to find the x-intercepts X2 + 8x + 12 = 0 -x2 + 4 = 0

6. Homework out