general form of a quadratic equation y = ax 2 + bx + c
DESCRIPTION
Standard Form ax 2 + bx + c = 0TRANSCRIPT
![Page 1: General Form of a Quadratic Equation y = ax 2 + bx + c](https://reader035.vdocuments.us/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972e2c/html5/thumbnails/1.jpg)
![Page 2: General Form of a Quadratic Equation y = ax 2 + bx + c](https://reader035.vdocuments.us/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972e2c/html5/thumbnails/2.jpg)
General Form General Form of a of a
Quadratic EquationQuadratic Equation
y = ax2 + bx + c
![Page 3: General Form of a Quadratic Equation y = ax 2 + bx + c](https://reader035.vdocuments.us/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972e2c/html5/thumbnails/3.jpg)
Standard Form
ax2 + bx + c = 0
![Page 4: General Form of a Quadratic Equation y = ax 2 + bx + c](https://reader035.vdocuments.us/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972e2c/html5/thumbnails/4.jpg)
Factoring and Solving• Rule 1 (the only rule)
– Find the G.C.F.– Otherwise, look for
something familiar
010112 xx
092 x
025102 xx
![Page 5: General Form of a Quadratic Equation y = ax 2 + bx + c](https://reader035.vdocuments.us/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972e2c/html5/thumbnails/5.jpg)
If factoring does not seem to be working…..
• Ask the following question:• “Is the linear term missing?”• If so, SQUARE ROOTS SEEM
GOOD.
052 x
![Page 6: General Form of a Quadratic Equation y = ax 2 + bx + c](https://reader035.vdocuments.us/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972e2c/html5/thumbnails/6.jpg)
Square Root Method• If you take the
square root of both sides of an equation, then you must get TWO answers.
39
92
2
xx
x
![Page 7: General Form of a Quadratic Equation y = ax 2 + bx + c](https://reader035.vdocuments.us/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972e2c/html5/thumbnails/7.jpg)
PERFECT SQUARED TRINOMIALS
• “FIRST TERM SQUARED PLUS TWICE THE FIRST TIMES THE LAST PLUS THE LAST TERM SQUARED.”
• Can be factored from a memorized formula.
222 )(2 bababa
![Page 8: General Form of a Quadratic Equation y = ax 2 + bx + c](https://reader035.vdocuments.us/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972e2c/html5/thumbnails/8.jpg)
Differences of Squares
• A difference of two squares can be factored.• Remember that the inner and outer terms
must be opposites.
))((22 bababa
![Page 9: General Form of a Quadratic Equation y = ax 2 + bx + c](https://reader035.vdocuments.us/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972e2c/html5/thumbnails/9.jpg)
A manufacturer determines that the number of drills it can sell is given by the formula where p is the price of the drills in dollars.
2851563 2 ppD
a. At what price will the manufacturer sell the maximum number of drills?
b. What is the maximum number of drills that can be sold?
![Page 10: General Form of a Quadratic Equation y = ax 2 + bx + c](https://reader035.vdocuments.us/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972e2c/html5/thumbnails/10.jpg)
![Page 11: General Form of a Quadratic Equation y = ax 2 + bx + c](https://reader035.vdocuments.us/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972e2c/html5/thumbnails/11.jpg)
Factor the expression.
xx 1410 2
)75(2 xx
![Page 12: General Form of a Quadratic Equation y = ax 2 + bx + c](https://reader035.vdocuments.us/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972e2c/html5/thumbnails/12.jpg)
102510 2 xx
)2)(12(5)252(5 2
xxxx
![Page 13: General Form of a Quadratic Equation y = ax 2 + bx + c](https://reader035.vdocuments.us/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972e2c/html5/thumbnails/13.jpg)
)6)(95(54215 2
xx
xx
![Page 14: General Form of a Quadratic Equation y = ax 2 + bx + c](https://reader035.vdocuments.us/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972e2c/html5/thumbnails/14.jpg)
254016 2 xx
2)54( x
![Page 15: General Form of a Quadratic Equation y = ax 2 + bx + c](https://reader035.vdocuments.us/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972e2c/html5/thumbnails/15.jpg)
4916 2 x
)74)(74( xx
![Page 16: General Form of a Quadratic Equation y = ax 2 + bx + c](https://reader035.vdocuments.us/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972e2c/html5/thumbnails/16.jpg)
Solve by factoring.
0320)7)(32(021112
0)21112(2
042224
2
2
2
xxxxx
xx
xx
07 xor
![Page 17: General Form of a Quadratic Equation y = ax 2 + bx + c](https://reader035.vdocuments.us/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972e2c/html5/thumbnails/17.jpg)
Solve the equation by finding square roots
87
644912898
98128
2
2
2
x
x
x
x
![Page 18: General Form of a Quadratic Equation y = ax 2 + bx + c](https://reader035.vdocuments.us/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972e2c/html5/thumbnails/18.jpg)
Solve the equation.
ixx
x
x
x
x
1
1
01
0)1(16
01616
2
2
2
2
![Page 19: General Form of a Quadratic Equation y = ax 2 + bx + c](https://reader035.vdocuments.us/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972e2c/html5/thumbnails/19.jpg)
Solve the equation.
414
5959
25)9(
2581182
2
xxxxx
xx
![Page 20: General Form of a Quadratic Equation y = ax 2 + bx + c](https://reader035.vdocuments.us/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972e2c/html5/thumbnails/20.jpg)
Solve by completing the square.
54
54
5)4(
1611168
0118
2
2
2
x
x
x
xx
xx
![Page 21: General Form of a Quadratic Equation y = ax 2 + bx + c](https://reader035.vdocuments.us/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972e2c/html5/thumbnails/21.jpg)
Solve by completing the square.
3649
3684)
67(
3649
37)
3649
37(
37)
37(
7)37(3
773
2
2
2
2
2
x
xx
xx
xx
xx
635
67
3635)
67(
3635)
67( 2
x
x
x
![Page 22: General Form of a Quadratic Equation y = ax 2 + bx + c](https://reader035.vdocuments.us/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972e2c/html5/thumbnails/22.jpg)
Rewrite in Vertex Form
2)5(
25232510
2310
2
2
2
xy
xxy
xxy
![Page 23: General Form of a Quadratic Equation y = ax 2 + bx + c](https://reader035.vdocuments.us/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972e2c/html5/thumbnails/23.jpg)
Rewrite in Vertex Form
7)25(53
375382)62550(53
3823053
2
2
2
xy
xxy
xxy