
Remediation 2.2 CFA Quadratic Formula
Presentation
•
Mathematics
•
11th Grade
•
Practice Problem
•
Easy
+1
Standards-aligned
Amanda Wood
Used 2+ times
FREE Resource
12 Slides • 23 Questions
1
The standard form of a quadratic equation is ax2+bx+c
What are the values for a, b and c in the following quadratic equations?
3x2+5x-1=0 2x2-7x=10
a=3, b=5, c=-1 a=2, b=-7, c=-10 (set = to 0)
2
Multiple Choice
a, b, and c for
the quadratic equation:
4x2 – 8x = 3
*remember right side should =0
3
Multiple Choice
Identify a, b, and c in: x2−6x+14
a=3,b=5,c=9
a=1,b=-6,c=14
a=1,b=-6,c=-14
a=1,b=6,c=14
4
5
Solving Quadratics ~ Process for Using the Quadratic Formula
6
Solving Quadratics ~ Example
7
Multiple Choice
What are the zeros of
f(x)=x2+7x−18 ?
x=−2, −9
x=2, −9
x=−2, 9
x=2, 9
8
Multiple Choice
Solve using the quadratic formula:
4x2 + 4x + 1 = 0
x = -½
x = -2
x = 0
x = ½
9
Multiple Choice
Use the quadratic formula to find the solutions for
y = -x2 - 5x + 12
No Real Solution
10
The Discriminant will tell you the number of solutions you have.
Discriminant = b2 - 4ac
11
If the discriminant is:
positive , then you have 2 real solutions
negative, then you have 2 complex solutions
zero - then you have one real solution (double root)
12
Multiple Choice
If the discriminant of the quadratic equation is equal to 0, how many real solutions are there?
None
One
Two
Infinite
13
Multiple Choice
If the discriminant of the quadratic equation is equal to 4, how many real solutions are there?
None
One
Two
Infinite
14
Multiple Choice
How many solutions does this equation have?
2 Real Solutions
1 Real Solution
2 Complex Solutions
15
Multiple Choice
What is the discriminant of 4x2+8x+6=0 AND what type of solutions does it have?
-32; 2 complex roots
32; 2 irrational roots
160; 2 irrational roots
16; 2 rational roots
16
Multiple Choice
5x2=10x−5
What is the discriminant of the equation AND what type of solutions does it have?
0; 1 rational root
0; 2 irrational roots
200; 2 irrational roots
200; 2 complex roots
17
Multiple Choice
and how many solutions does the function have?
discriminate = -71 and two complex solutions
discriminate = -121 and has two complex solutions
the discriminate = - 71 and has two real solutions
the disctiminate = -121 and has two real solutions
18
Applications
When solving application problems dealing with quadratics, set the equation equal to 0 and use the quadratic formula. Make sure to check your answers. Choose the answer that makes sense!
If you are finding how many seconds it will take for a ball to reach the ground, you will not choose the negative solution!
19
Multiple Choice
6 seconds
20
Multiple Choice
A frog is sitting on the ground when he is scared by a big dog. His movement is modeled by the equation h = -6t2 + 6t where h is the frog's height at any given time, t . How many seconds until the frog is back on the ground?
0.5 seconds
1 second
1.5 seconds
2 seconds
3 seconds
21
Multiple Choice
The function f(t) = -5t2+20t + 60 models the approximate height of an object t seconds after it is launched. How many seconds does it take the object to hit the ground?
4 seconds
2 seconds
6 seconds
9 seconds
22
Complex Numbers
Learning Target: I can simplify expressions with complex numbers.
23
Multiple Choice
Solve using the quadratic formula.
r2−2r+4=0
{1}
{1+i3, 1−i3}
{1.618, −0.618}
{21+i3, 21−i3}
24
Multiple Choice
Solve using the quadratic formula. f(x)=2x2−4x+7
22±2i10
44±40
22±i10
42±2i40
25
Adding Complex Numbers
When adding complex numbers
-Add real parts together
-Add imaginary parts together
26
Multiple Choice
Find the sum.
(5-2i) + (-7+8i)
-2+6i
12+6i
-35-16i2
-35 -16i
27
Subtracting Complex Numbers
Distribute the negative
Add real parts together
Add imaginary parts together
28
Multiple Choice
Simplify:
(10+ 15i) - (48 - 30i)
58 - 45i
58 - 15i
-38 - 15i
-38 + 45i
29
Multiplying Complex Numbers
Use an area model.
Multiply to get insides
Add like terms
simplify i2
Write as a sum
30
Multiple Choice
-3i(4 + 2i)
31
Multiple Choice
(2 - 3i)(5 + 4i)
32
Multiple Choice
(-6 - 2i)2
33
Imaginary Numbers
34
Multiple Choice
Simplify
√-4
2i
-2i
2
4i
35
Multiple Choice
The standard form of a quadratic equation is ax2+bx+c
What are the values for a, b and c in the following quadratic equations?
3x2+5x-1=0 2x2-7x=10
a=3, b=5, c=-1 a=2, b=-7, c=-10 (set = to 0)
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