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Properties of Parabolas that open Up or Down General Form: y = ax2+bx+c
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Properties of Parabolas that open Up or Down General Form: y = ax2+bx+c
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Properties of Parabolas that open Up or Down General Form: y = ax2+bx+c Standard form (also called vertex form) is y = a(x - h)2 + k, where the vertex is (h,k) If a is positive it opens up If a is negative it opens down Axis of Symmetry (aos) is x = -b/2a
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Properties of Parabolas that open Right or Left
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Properties of Parabolas that open Right or Left General Form: x = ay2+by+c
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Properties of Parabolas that open Right or Left General Form: x = ay2+by+c
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Properties of Parabolas that open Right or Left General Form: x = ay2+by+c Standard Form: x = a(y – k)2+ h, where the vertex is (h,k) If a is positive it opens right If a is negative it opens left
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Properties of Parabolas that open Right or Left General Form: x = ay2+by+c Standard Form: x = a(y – k)2+ h, where the vertex is (h,k) If a is positive it opens right If a is negative it opens left Axis of Symmetry (aos) is y = -b/2a
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Differences Properties of Parabolas that open Left or Right
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Differences Properties of Parabolas that open Left or Right x=
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Differences Properties of Parabolas that open Left or Right x= aos: y =
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Differences Properties of Parabolas that open Left or Right x= aos: y = vertex is (h,k)
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Differences Properties of Parabolas Properties of Parabolas that open Up or Down: that open Left or Right y= x= aos: x = aos: y = Vertex is (h,k) vertex is (h,k)
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Examples :Tell the direction that each parabola opens, the vertex and the axisof symmetry (aos). 2 2 y = 5 ( x + 2) − 6 x = −2 ( y + 1) + 1
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Examples :Tell the direction that each parabola opens, the vertex and the axisof symmetry (aos). 2 2 y = 5 ( x + 2) − 6 x = −2 ( y + 1) + 1 Opens up
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Examples :Tell the direction that each parabola opens, the vertex and the axisof symmetry (aos). 2 2 y = 5 ( x + 2) − 6 x = −2 ( y + 1) + 1 Opens up Vertex is (-2,-6) make sure to change the sign of the value in the parenthesis
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Examples :Tell the direction that each parabola opens, the vertex and the axisof symmetry (aos). 2 2 y = 5 ( x + 2) − 6 x = −2 ( y + 1) + 1 Opens up Vertex is (-2,-6) make sure to change the sign of the value in the parenthesis aos is x = -2 once you have found the vertex you can just take the x coordinate and that is your aos
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Examples :Tell the direction that each parabola opens, the vertex and the axisof symmetry (aos). 2 2 y = 5 ( x + 2) − 6 x = −2 ( y + 1) + 1 Opens up Opens left Vertex is (-2,-6) make sure to change the sign of the value in the parenthesis aos is x = -2 once you have found the vertex you can just take the x coordinate and that is your aos
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Examples :Tell the direction that each parabola opens, the vertex and the axisof symmetry (aos). 2 2 y = 5 ( x + 2) − 6 x = −2 ( y + 1) + 1 Opens up Opens left Vertex is (-2,-6) vertex: (1,-1) make sure to change the sign of the value in the parenthesis aos is x = -2 once you have found the vertex you can just take the x coordinate and that is your aos
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Examples :Tell the direction that each parabola opens, the vertex and the axisof symmetry (aos). 2 2 y = 5 ( x + 2) − 6 x = −2 ( y + 1) + 1 Opens up Opens left Vertex is (-2,-6) vertex: (1,-1) make sure to change the sign of the value in the The thing to remember parenthesis here is that the y- coordinate is now in the aos is x = -2 parenthesis and the x – once you have found the coordinate is in the back. vertex you can just take the x coordinate and that is your aos
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Examples :Tell the direction that each parabola opens, the vertex and the axisof symmetry (aos). 2 2 y = 5 ( x + 2) − 6 x = −2 ( y + 1) + 1 Opens up Opens left Vertex is (-2,-6) vertex: (1,-1) make sure to change the sign of the value in the The thing to remember parenthesis here is that the y- coordinate is now in the aos is x = -2 parenthesis and the x – once you have found the coordinate is in the back. vertex you can just take aos: y = -1 the x coordinate and that is your aos
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Putting an Equation in Standard Form Complete the square.
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Putting an Equation in Standard Form Complete the square. Example: y = x2 - 2x + 4 y = (x2 - 2x + ___ ) + 4 – (a) ___ put (-b/2)2 in the blanks and the value for a in the parenthesis before the last blank y = (x2 - 2x + (2/2)2 ) + 4 – (1)(2/2)2 y = (x2 -2x + 1) + 4 – (1)(1) now factor the first set of () y = (x - 1)2 + 4 – 1 y = (x - 1)2 + 3 now it easy to find the vertex and aos.
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Determine the direction in which the following open.Solve for either x or y whichever one is only in the problem once or is notsquared. 2 2 6x + 2y + 4x = 10 10y − 5y − 5x + 10 = 0
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Determine the direction in which the following open.Solve for either x or y whichever one is only in the problem once or is notsquared. 2 2 6x + 2y + 4x = 10 10y − 5y − 5x + 10 = 0 Solve for y 2y = -6x2 – 4x +10 y = -3x2 -2x + 5
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Determine the direction in which the following open.Solve for either x or y whichever one is only in the problem once or is notsquared. 2 2 6x + 2y + 4x = 10 10y − 5y − 5x + 10 = 0 Solve for y 2y = -6x2 – 4x +10 y = -3x2 -2x + 5 Opens down
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Determine the direction in which the following open.Solve for either x or y whichever one is only in the problem once or is notsquared. 2 2 6x + 2y + 4x = 10 10y − 5y − 5x + 10 = 0 Solve for y Solve for x 2y = -6x2 – 4x +10 y = -3x2 -2x + 5 Opens down
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Determine the direction in which the following open.Solve for either x or y whichever one is only in the problem once or is notsquared. 2 2 6x + 2y + 4x = 10 10y − 5y − 5x + 10 = 0 Solve for y Solve for x 2y = -6x2 – 4x +10 -5x = 5y2 – 10y -10 y = -3x2 -2x + 5 Opens down
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Determine the direction in which the following open.Solve for either x or y whichever one is only in the problem once or is notsquared. 2 2 6x + 2y + 4x = 10 10y − 5y − 5x + 10 = 0 Solve for y Solve for x 2y = -6x2 – 4x +10 -5x = 5y2 – 10y -10 y = -3x2 -2x + 5 x = - y2 + 2y + 2 Opens down
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Determine the direction in which the following open.Solve for either x or y whichever one is only in the problem once or is notsquared. 2 2 6x + 2y + 4x = 10 10y − 5y − 5x + 10 = 0 Solve for y Solve for x 2y = -6x2 – 4x +10 -5x = 5y2 – 10y -10 y = -3x2 -2x + 5 x = - y2 + 2y + 2 Opens down Opens left
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Write the Standard Form of the equation with a Vertex at (-1,2) and goes through the point (2, 8).
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Write the Standard Form of the equation with a Vertex at (-1,2) and goes through the point (2, 8). Identify h, k , x and y h = -1, k = 2 these are from the vertex x = 2, y = 8 these are from the other point
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Write the Standard Form of the equation with a Vertex at (-1,2) and goes through the point (2, 8). Identify h, k , x and y h = -1, k = 2 these are from the vertex x = 2, y = 8 these are from the other point Plug in what you know y = a(x - h)2 + k 8 = a(2 – (-1))2 + 2
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Write the Standard Form of the equation with a Vertex at (-1,2) and goes through the point (2, 8). Identify h, k , x and y h = -1, k = 2 these are from the vertex x = 2, y = 8 these are from the other point Plug in what you know y = a(x - h)2 + k 8 = a(2 – (-1))2 + 2 Now solve for a 8 = 9a + 2 6 = 9a 6/9 = a or a = ⅔
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Write the Standard Form of the equation with a Vertex at (-1,2) and goes through the point (2, 8). Identify h, k , x and y h = -1, k = 2 these are from the vertex x = 2, y = 8 these are from the other point Plug in what you know y = a(x - h)2 + k 8 = a(2 – (-1))2 + 2 Now solve for a 8 = 9a + 2 6 = 9a 6/9 = a or a = ⅔ Write the answer in Standard Form, plugging in a h and k y = ⅔(x + 1)2 + 2
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