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Quadratics

Quadratics. By: Ou Suk Kwon. How can Factor Polynomials?. In Algebra there are many ways to Factor the Polynomials, but the most common one is. First find any variable or number that can be solved by GCF. Then multiply A and C, most of the time A is 1.

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Quadratics

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  1. Quadratics By: OuSuk Kwon

  2. How can Factor Polynomials? • In Algebra there are many ways to Factor the Polynomials, but the most common one is. • First find any variable or number that can be solved by GCF. • Then multiply A and C, most of the time A is 1. • Then find 2 secret numbers that add up to B and multiply to give the answer of A times C. • Then replace these 2 numbers over A. • Then simplify or reduce it.

  3. Examples of Factoring Polynomials • x^2+7x+10=0 A x C = 10 so we have to find 2 numbers that add up to 7 and Multiply give us 10. So the answer for this one is +5 and +2. • x^2+10x+25=0 A x C = 25 and B= 10 so the answer is +5 and +5. • x^2+12x-45 A x C =-45 and B= 12 so the answer is +15 and -3

  4. Quadratic function • A quadratic function is a function that is shown in an equation that is x=ax^2+bx+c. A never can equal to zero. • The difference between a quadratic function and a linear function is that a linear graphs a line in the graph and the Quadratic functions graph a parabola in the graph. differences: • A quadratic function always has to be squared • In linear function you are trying to find only one value of variable, which is X. • The function of linear is y=mx+b and Quadratic is Ax^2+bx+c.

  5. Quadratic Function(Graph) • Your graphing formula always looks like A(x+B) ^2+C=0. A) A in the graph, always is going to be a slope of the parabola. A is making the parabola to face down(-) or up(+). Also the value of the A changes the steepness of the parabola. If A > 0, then the parabola will be steeper, but when A < 0 then the parabola will be less steep.

  6. B and C are the ones that changes the place of the vertex of the parabola. B is the value of X-axis and C is the value of Y-Axis. B) As B changes in the X-axis, B changes the vertex to right or left. One thing that you have to be careful is that, B always changes to opposite way. When the value of B is negative, the vertex moves to right. B can be called P too. C) C moves the vertex up or down, also C can be called Q.

  7. Examples X^2 2(x-4)^2+3

  8. Solving quadratics using graphing method • The first thing that you must do is to put ax^2+bx+c equal to zero. • Then make a T-table. • When you are making your t-table, you should found the vertex first. To find the vertex you must use -B/2A this formula. • After completing with the t-table, you must choose 2 points in the left to draw the same points in the right. • After that, connect all the dots and make the parabola. The points that are on the X-axis, those are the answers of the quedratic.

  9. Y=x^2 y=1/3x^2 Y=3x^2

  10. Solving quadratic using square roots • I guess solving quadratic using square root is the easiest way to solve the quadratics. • In square roots you just have to add a square root sign to both sides of the equation • And square root the variable and the number that has to be squared. • Always remember about + and -

  11. Examples • X^2=121 x=11 • X^2=4 X=2 • X^2=225 X=15

  12. Completing the square • Get x^2 = 1 • Then get C by itself • Complete the square • After that find (b/2)^2 and add to the both sides of the equation. • Then simply square rood both sides, don’t forget about + and -

  13. Example • X^2+4x+10=2 X^2+4x=-8+4 (X+2)^2=-8+4 X+2=+-2 X= -4, 0

  14. X^2+16x+6=16 X^2+16x=10 (x+4)^2=10+4 X+4=+- root14 X=-4-root14, -4+root14

  15. X^2+25x+4=8 X^2+25x=4 (X+5)^2=4+25/4 X+5= +- 2root 25/4 X=-5-2root 25/4, -5+2root 25/4

  16. Solving Quadratic using the Formula. • First think that you have to do in the formula is to find A, B, and C. • When you found all of them, you should plug it in to these formula

  17. Example • X^2+4x+6 • A=1 B=4 C=6 So -4+-root16-24/2 • X^2+2x+5 A=1 B=2 C=5 So -2+-root4-20/2

  18. X^2+3x-2 A=1 B=3 C=-2 -3+-root9+8/2

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