1. Identify the vertex. tell minimum or maximum.
y=-3x^2
2.y=5x^2+1
3.order from widest to narrowest graph.
y=x^2,y=5x^2,y=3x^2
4.y=-8x^2,y=1/2x^2,y=-x^2
5. graph each function. just say coordinates
y=x^2
6. y=2x^2-2
y=-3x^2
2.y=5x^2+1
3.order from widest to narrowest graph.
y=x^2,y=5x^2,y=3x^2
4.y=-8x^2,y=1/2x^2,y=-x^2
5. graph each function. just say coordinates
y=x^2
6. y=2x^2-2
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1. y = -3x^2 will have a vertex at (0,0). It is a maximum, because the -3 makes the parabola go downward.
2. y = 5x^2 + 1 will have a vertex at (0,1). It is a minimum, because the 5 makes the parabola go upward (y increases with increasing absolute value of x).
3. y = x^2 is the widest, because if you put in for example x=5, y will be 25. y = 5x^2, on the other hand, x=5 gives y=125. As a result, the graph must increase on the y axis much faster in y = 5x^2, making the graph more narrow. The order then is: y = x^2, y = 3x^2, y = 5x^2
4. y = 1/2 x^2, y = -x^2, y = -8x^2 (same principle as 3, with the graphs just going downward with there is a - before an x).
5. x = 0 gives y = 0 (vertex). x = 1 gives y = 1 (1,1). x = -1 also gives y = 1. Now you have two sides to the parabola. x = 2 and x = -2 both give y = 4, so you have two more points, (-2, 4) and (2, 4). x = 3 and x = -3 give (-3, 9) and (3, 9). Etc.
6. The graph is shifted down -2, so the vertex is at (0, -2). x = 1 and x = -1 give the first two points, (-1, 0) and (1, 0). x = -2 and x = 2 gives (-2, 6) and (2, 6). x = -3 and x = 3 gives (-3, 16) and (3, 16). Etc.
2. y = 5x^2 + 1 will have a vertex at (0,1). It is a minimum, because the 5 makes the parabola go upward (y increases with increasing absolute value of x).
3. y = x^2 is the widest, because if you put in for example x=5, y will be 25. y = 5x^2, on the other hand, x=5 gives y=125. As a result, the graph must increase on the y axis much faster in y = 5x^2, making the graph more narrow. The order then is: y = x^2, y = 3x^2, y = 5x^2
4. y = 1/2 x^2, y = -x^2, y = -8x^2 (same principle as 3, with the graphs just going downward with there is a - before an x).
5. x = 0 gives y = 0 (vertex). x = 1 gives y = 1 (1,1). x = -1 also gives y = 1. Now you have two sides to the parabola. x = 2 and x = -2 both give y = 4, so you have two more points, (-2, 4) and (2, 4). x = 3 and x = -3 give (-3, 9) and (3, 9). Etc.
6. The graph is shifted down -2, so the vertex is at (0, -2). x = 1 and x = -1 give the first two points, (-1, 0) and (1, 0). x = -2 and x = 2 gives (-2, 6) and (2, 6). x = -3 and x = 3 gives (-3, 16) and (3, 16). Etc.
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1. y=-3x^2
not minimum, but maximum is y=0 at x=0
2.y=5x^2+1
not maximum, but minimum is y = 1 at x =0
3.order from widest to narrowest graph.
y=x^2, y=3x^2, y=5x^2,
4.y=1/2x^2, y=-x^2, y=-8x^2
5. graph each function. just say coordinates
y=x^2 , (0;0), (1;1), (-1;1), (2;4), (-2;4), top min is (0;0)
6. y=2x^2-2, (0;-2), (1;0), (-1;0), (2;6), (-2;6) top min is (0;-2)
not minimum, but maximum is y=0 at x=0
2.y=5x^2+1
not maximum, but minimum is y = 1 at x =0
3.order from widest to narrowest graph.
y=x^2, y=3x^2, y=5x^2,
4.y=1/2x^2, y=-x^2, y=-8x^2
5. graph each function. just say coordinates
y=x^2 , (0;0), (1;1), (-1;1), (2;4), (-2;4), top min is (0;0)
6. y=2x^2-2, (0;-2), (1;0), (-1;0), (2;6), (-2;6) top min is (0;-2)
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1. (0,0), minimum
2. (0,1), minimum
3. y=x^2,y=3x^2,y=5x^2
4. y=-(1/2)x^2,y=-x^2,y=-8x^2 (I guess it is -1/2, for +1/2, it is the same width, but upward)
5. (-2, 4), (-1, 1), (0, 0), (1, 1), (2, 4)
6. (-2, 6), (-1, 0), (0, -2), (1, 0), (2, 6)
2. (0,1), minimum
3. y=x^2,y=3x^2,y=5x^2
4. y=-(1/2)x^2,y=-x^2,y=-8x^2 (I guess it is -1/2, for +1/2, it is the same width, but upward)
5. (-2, 4), (-1, 1), (0, 0), (1, 1), (2, 4)
6. (-2, 6), (-1, 0), (0, -2), (1, 0), (2, 6)