1. The Quadratic Formula

2. Solve Quadratic Equations:
What about…
4x = 0
-x2 = -2x - 3
4x2 = 100
x2 = 25
We can’t combine like terms when there is an x2 and x term – need to use a new formula!
x = ±5

3. Quadratic Formula: To Solve Use the Quadratic Formula:
write the equation in standard form
set the function equal to 0
Plug in a, b, and c values and simplify

4. Quadratic Equation Solutions:
You could get two solutions, one solution, or no solutions
The solutions are the x intercepts (called “zeros” of the function)
Plugging in a 0 for the y (set the equation = 0) gives x intercepts

5. Use Quadratic Formula to Solve:
Ex. 1
y-x2 = -2x-3
1. Write in standard form y=ax2+bx+c
+x2 +x2
2. Make sure function is set = 0 (This is standard form with a 0 instead of y)
y = x2 -2x - 3
0 = x2 -2x - 3
a=1 b=-2 c=-3
3. Plug in a, b, c values and simplify
Work continued…

6. Use Quadratic Formula to Solve:
Plug in a=1 b=-2 c=-3, and simplify
x = 3 and -1
x ints (3,0) and (-1,0)

7. Use Quadratic Formula to Solve:
Ex. 2
x2+5x = 14
1. Write in standard form y=ax2+bx+c
2. Make sure function is set = 0 (This is standard form with a 0 instead of y)
x2+5x-14 = 0
a=1 b=5 c=-14
3. Plug in a, b, c values and simplify
Work continued…

8. Use Quadratic Formula to Solve:
Plug in a=1 b=5 c=-14, and simplify
x = 2 and -7
x ints are (2,0) and (-7,0)

9. Clear out - in front of a by multiplying both sides by -1
Ex. 3
Solve:
Clear out - in front of a by multiplying both sides by -1
0= x2+2x-5

10. Rationalize answer if not perfect squares

11. Practice saying the Quadratic Equation…
Sing along with the clip!

12. REAL LIFE:
If you throw a rock straight down from a cliff at a speed of 30ft./sec., how soon will it hit the ground?
1050 ft.

13. Set h=0 when rock hits ground
Formula:
h=-16t2+vt+s
h= height at time t
t= time in seconds
s= starting height in feet
v= velocity (ft/sec.) falling is -
Set h=0 when rock hits ground
0=-16t2+vt+s
0=-16t2+(-30)t+1050

14. And

15. Can’t have - seconds