| ax2+bx+c - If the coefficient of the x2 term is positive it has a mimimum point. - If the coefficient of the x2 term is negative it has a maximum point. |
| ax2+bx+c - If the coefficient of the x term gets larger the graph shifts left. |
| ax2+bx+c - If the constant gets larger the graph shifts upward. - If the constant gets smaller the graph shifts downward. |
| ax2+bx+c - If a gets smaller th graph becomes wider. - If a gets bigger the graph becomes thinner. |
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| What things do you know from its factored form? From its factored form you can find the intercepts (roots) on a graph these spots are where the lines touch the x and y axis. (x-4) (x+1) First you must make each equation equal 0. x-4 = 0 +4 +4 Add 4 because -4+4 = 0, so x = 4 x= 4 x+1 = 0 Here you subtract 1 because 1-1=0, so x = -1 -1 -1 x = -1 4,0 and -1,0 are where the intercepts on the graph are found for (x-4)(x+1) |
| (x-9)(x+2) x-9=0 x+2=0 +9 +9 -2 -2 x=9 x=-2 (9,0)&(-2,0) (x-5)(x+10) x-5=0 x+10=0 +5 +5 -1 -10 x= 5 x =-10 (5,0)(-10,0) |
| To change from standard to factored , make a box. x2+8x+12 |
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| Place the equationsinside of the box's. Since x*x is x2 place an x on tops of the box labeled x2 and to the left of it. |
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| Since x*6 will equal 6x, place 6 on top of the box labeld 6x and put 2 to the left of the box labeled 2x because 2*x=2x |
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| Now you hae the factored form to x2+8x+12 which is (x+6)(x+2) |
| x2+4x+3 |
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| When you put 3 and 4x into the box's remember these (red) 2 box's times eachother must equal (blue) that box and when added together they must equal 4 in this case. |
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| SO..... |
| 4x = 1x+3x 3 = 1x3 (x+1)(x+3) |
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| x2-8x+16 |
| -4x+ -4x = -8x -4x*-4x =16 (x-4)(x-4) |
| What things do you know from its vertex form? Where the highest or lowest point on the graph will be. x2-4x+8 |
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| Make a box -4 should ALWAYS be divided by 2 , -4x/2=-2x andthen plaedin the 2 red boxes. Then -2*-2=4. 4 should be subtraced from 8 in x2-4x+8 8-4=4 a(x+h)2+k this is where the vertez is found h=-2 and k=4 K should stay the same bu h should change to a positive if its a negative or if its a negative it should change to a positive. So.... h=-2 --> +2 k=4 vertex is at 2,4 |
| a(x+h)2+k x2+8+20 |
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| 8/2=4 4*4=16 20-16=4 h=4= -4 k=4 vertex - 4,4 |
| x2-2x+10 |
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| -2x/2 =-1x 10-1=9 h= -1x = 1x k=9 Vertex - 1,9 |