9.6 Applications of the Discriminant
Obj ­ Use the discriminant to find the number of solutions of a
quadratic equation. Apply the discriminant to solve real life problems
Quadratic Formula x = ­b ± √(b
2a
2
­ 4ac)
b 2 ­ 4ac is called the discriminant.
We used the quadratic formula to find the x­intercepts of a graph.
We didn't cover the special cases. What happens if the graph doesn't cross the x­axis? What happens if the vertex is on the x­
axis? The number of solutions of a quadratic equation:
If b 2 ­ 4ac is positive, then the equation has two solutions (graph crosses the x­axis 2 times)
If b 2 ­ 4ac is negative, then the equation has no real solutions
(graph never crosses the x­axis)
If b 2 ­ 4ac is zero, then the equation has one solution
(vertex is on x­axis)
1
Find the value of the discriminant and use the value to tell if the equation has 2, 1 or no solutions.
a) x
2
­ 3x = 4 b) x
2
= 2x ­ 1
c) 2x
2
­ 2x + 3 = 0
2
Sketch a graph of each function
on the same coordinate plane. a) y = x
b) y = x
c) y = x
2
+ 2x ­ 2
+ 2x + 1
2
+ 2x + 3
2
3
You and a friend are camping in Glacier National Park in Montana. You want to hang a food pack from a high tree branch in order to protect your food from bears. You attach a stick to a rope and your friend is preparing to throw it over a tree branch that is 20 feet from the ground. a) Your friend can throw the stick upward with an initial velocity of 29 feet per second from an initial height of 6 feet. Will the
stick reach the branch when it is thrown? b) You can throw a stick upward with an ititial velocity of 32 feet
per second from the same initial height as your friend. Will the stick reach the branch when it is thrown?
4
Read the problems. If you are asked a question about can it be done? On these types of questions you just need to use the discriminant. If the discriminant is positive ­ the situation will work.
If the discriminant is negative ­ the situation won't work.
If the discriminant is zero ­ you have to think about the situation.
5
Assignment ­ 9.6
page 544 12 ­ 20
24 ­ 26
42 ­ 44
page 547 7 ­ 11
6
7