Transcript 3.6-3.8-solve quad-sq rt-disc

Math I
UNIT QUESTION: What is a
quadratic function?
Standard: MM2A3, MM2A4
Today’s Question:
How do you solve quadratic
equations that can’t be factored?
Standard: MM2A4.b.
DAY ONE
3.6 - Solving a Quadratic Equation by Square Roots
Let’s look at some
examples where
2
x is already by
itself.
Examples. Solve the equation. Write the solutions as
integers if possible. Otherwise, write them as radical
expressions.
2
2
1. x  4
x
2
 4
x  2
2. n  5
n  5
2
n 5
You try :
1. x  81
2
2. y  11
2
3. c  25
2
4. x  10
2
Let’s look at some
examples where
2
x is NOT by itself.
We must solve to get x2 by itself 1st!
3x  48  0
2
3 x  48
2
x  16
2
x  4
We must solve to get x2 by itself 1st!
x  32  96
2
x  64
2
x  8
You try!
x 1  0
2
2 x  72  0
2
Falling object model
When an object is dropped, the speed with which it
falls continues to increase. Ignoring air resistance,
its height h can be approximated by the falling
object model:
h  16t  s
2
An engineering student is a contestant in an egg dropping
contest. The goal is to create a container for an egg so it can
be dropped from a height of 32 feet without breaking (s =
starting height). Find the time (t) it will take for the egg to hit
the ground (height = ? ). Disregard air resistance.
h  16t  s
2
SOLUTION:
0  16t  32
2
 32  16t
2
2t
t
2
2  1.4
The starting height is 32 feet.
Now, substitute 0 for h and solve.
Subtract 32 from both sides
Divide both sides by –16
Take the square root of both sides
So, the answer is 1.4 seconds. It is
only the positive of the square root b/c
you can’t have negative seconds!!!!! 
DAY TWO
The following quadratics are in standard form,
ax2 + bx + c
Evaluate b2 – 4ac for each of the following
1)x2 – 3x + 2
1
2)x2 – 4x + 4
0
3)2x2 – 3x + 3
-15
There is a way to tell how many
roots an equation will have.
It’s called finding the discriminant.
The discriminant is a small part of the
quadratic formula.
b  4ac
2
b  4ac
2
If the answer is POSITIVE, then you will have 2 roots.
If the answer is ZERO, then you will have 1 root.
If the answer is NEGATIVE, then you will have no roots.
Our text book says solutions instead of roots (same thing).
Determine the number of roots.
Example: 1
x  3x  4  0
2
b  4ac  ( 3)  4(1)(4)
 9  16
 7
2
2
Determine the number of roots.
Example: 2
x  4x  4  0
2
b  4ac  ( 4)  4(1)(4)
 16  16
0
2
2
Determine the number of roots.
Example: 3
x  5x  4  0
2
b  4ac  ( 5)  4(1)(4)
 25  16
9
2
2
Find the number of x-intercepts.
Example: 4
y  x  4x  3
2
b  4ac  ( 4)  4(1)(3)
2
2
 16  12
4
Find the number of x-intercepts.
Example: 5
y  x  2x  3
2
b  4ac  (2)  4(1)(3)
 4  12
2
2
 8
Solve for x:
x  25  0
2
x  9 x  14  0
2
Quadratic Formula: gives the solution of
2
ax  b
bx  c  0 in terms of the
a
coefficients a, b & c.
The solutions of the quadratic equation are
bb  bb  4a
acc
x
2a
2
Ex: 1 Solve x2+ 9x +14 = 0
1st
 b  b  4ac  9  9  4 114

x
2 1
2a
a=
 9  81  4 114  9  2nd
81

56


b=
2 1
2
2
c=
2
 9  25  9  5   9  5 and  9  5


2
2
2
2
4
 14

and
 2 and  7
2
2
x  4x  3  0
2
1.)2 x  x  10  0
2
2.)  x 2  3 x  4  0
3.)2 x 2  3 x  8
-5/2 & 2
-1 & 4
2.89 & -1.39
A rocket is shot upward with an initial velocity of 125 feet
per second from a platform 3 feet above the ground. Use
2
the model
to find how long
h  16t  vt  s
it will take the rocket to hit the ground.
t = 7.83 seconds
3 ft
HOMEWORK 