Solve Quadratics with Square Roots
Solving Quadratic Equations by Finding Square Roots
Focus 9 Learning Goal –
( HS.A-SSE.A.1, HS.A-SSE.A.2, HS.A-SEE.B., HS.A-APR.A.1, HS.A-
APR.B.3, HS.A-REI.B.4)
= Students will factor polynomials using multiple methods, perform operations (excluding division) on polynomials and sketch rough graphs using key features.
4
In addition to level 3, students make connections to other content areas and/or contextual situations outside of math.
3
Students will factor polynomials using multiple methods, perform operations
(excluding division) on polynomials and sketch rough graphs using key features.
- Factor using methods including common factors, grouping, difference of two squares, sum and difference of two cubes, and combination of methods.
- Add, subtract, and multiply polynomials,
- Explain how the multiplicity of the zeros provides clues as to how the graph will behave.
- Sketch a rough graph using the zeros and other easily identifiable points.
2
Students will factor polynomials using limited methods, perform operations
(excluding division) on polynomials, and identify key features on a graph.
- Add and subtract polynomials.
- Multiply polynomials using an area model.
- Factor polynomials using an area model.
- Identify the zeros when suitable factorizations are available.
- Identify key features of a graph.
1
Students will have partial success at a 2 or 3, with help.
0
Even with help, the student is not successful at the learning goal.
Remember: Linear equation is x to the first power ax+by=c
Quadratic equation: is x to the second power
Standard Form:
ax
2
+bx+c=0
a
0
Find Solutions to ax
2
+c=0
(Get x
2
alone in form x
2
=d)
Once you get x
2
=d take the square root of both sides to get x.
3 Results
1. x 2 =d If d is a positive number, then you have 2 solutions x
d
2. x 2 =d If d=0 then there is only one solution x=0
3. x 2 =d If d is a negative number, there is no solution
(Can’t take sq. root of a negative)
1.
Examples:
2.
x 2 =4 x 2
x
x 2 =5
4 x 2
2 x
x can be + or -, when squared it is positive
5
5
Solve:
4x 2 + 100 = 0
-100 -100
4x 2 = -100 x 2 = -25
(divide both sides by 4)
NO Solution
3x 2 -99 = 0
3x 2 = 99 x 2 = 33 x
33
Two Solutions
The surface area of a cube is 150ft 2 . Find the length of each edge.
SA = 6s 2 x x x
Sides of the cube are 5 ft.
You can’t have a negative length.
150 = 6s 2
25 = s 2
5
s
1st
DIVIDE
BY 6
Watch out below!
A construction worker on the top floor of a 200 foot tall building accidentally drops a heavy wrench. How many sections will it take to hit the ground?
The formula d=rt is used when the speed is constant. However, when an object is dropped, the speed continually increases.
Use the formula: h = -16t 2 + s h = final height of object t = time s = starting height of object h = -16t 2 + s
0 = -16t 2 + 200
-200 = -16t 2
12.5 = t 2
√12.5 = t
About 3.54 seconds.
