Download 4.8 Use the Quadratic formula and the discriminant Goal: To

4.8 Use the Quadratic formula and the discriminant
Goal: To complete the square and find the roots of the equation
State Standard: 8.11.18
"b ± b 2 " 4ac
Quadratic formula- x =
2a
Note- To use the formula you must have the equation set equal to zero
! the equation
Ex. 1 Solve
a. x2 = 6x - 4
b. 4x2 – 10x = 2x – 9
c. 7x – 5x2 – 4 = 2x + 3
Def
1) Discriminant- what is under the square root in the quadratic formula
Note
1) If the discriminant is greater than 0, then there will be two real solutions
2) If the discriminant is equal to 0, then there will be one real solution
3) If the discriminant is less than 0 then there will be two imaginary solutions
Ex. 2 Find the discriminant of the quadratic equation and give the number and type of solutions of the
equation
a) x2 - 8x + 17 = 0
b) 2x2 + 4x - 4 = 0
c) 8x2 = 9x - 11
Thrown object model- h = -16t2 + vt + h0 where v is the initial velocity
Ex. 3 Find the time of flight of a ball that was thrown with a initial velocity of 40 ft/s at three feet high.
HWK p. 296- 299 1-46 every third, 69, 71