Download 7x+16=0 b 2 -4ac

Problem Solving
Using the
Discriminant
Quadratic Equation:
2
 b  b  4ac
x
2a
Discriminant:
2
b -4ac
If b2-4ac is positive, then 2 solutions
If b2-4ac is 0, then 1 solution
If b2-4ac is negative, then no solution
If you find the discriminant, you
can tell whether or not you will
have a solution.
Find the discriminant and
number of solutions for:
3x2+4x-5=0
b2-4ac
42-4(3)(-5)
16+60
76
2 Solutions
2
x -7x+16=0
b2-4ac
(-7)2-4(1)(16)
49-64
-15
No Solution
Equations:
Object dropped
h=-16t2+s
Object thrown
h=-16t2+vt+s
You are standing beneath a ledge
that is 15 ft. high. If you throw a
rope up at a velocity of 30 ft/sec.,
will it reach the ledge?
Which
2+30t+0
15=-16t
equation?
0=-16t2+30t-15
Find discriminant to see
if there is a solution
before solving.
2
b -4ac
302-4(-16)(-15)
900-960
-60
NO SOLUTION
You must throw it harder
Try this one
• Rick is a firefighter and is leaning out a
window on the eighth floor. He is trying to
throw a grappling hook to a tenth-floor
window that is 26 feet above him.
• Rick can throw the grappling hook with a
maximum speed of 40 feet per second. Can
he throw the grappling hook to the window
above him?
Which formula do you need?
•
•
•
•
•
•
•
•
h = -16t2 + vt + s
Plug in what you know and solve.
26 = -16t2 + 40t + 0
0 = -16t2 + 40t - 26
b2-4ac
402 – 4(-16)(-26)
1600 – 1664
-64
Answer:
• The discriminate is -64, so he cant
throw it high enough.
• If he could throw it a little faster or
if the window were a little closer, he
could make it.