The form of a parabola is shown in this picture:
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Notice the the parabola a heat of symmetry, definition the 2 sides winter each other.There space two patterns for a parabola, as it have the right to be one of two people vertical (opens increase or down) or horizontal (opens left or right.)Patterns:
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Let"s look at a few key points around these patterns:
If the x is squared, the parabola is vertical (opens up or down). If the y is squared, it is horizontal (opens left or right).If a is positive, the parabola opens up up or to the right. If it is negative, it opens up down or to the left.The vertex is in ~ (h, k). You have to be very careful. An alert how the ar of h and also k switches based on if the parabola is vertical or horizontal. Also, the coordinate inside the parenthesis is negative, but the one outside is not.

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Let"s look in ~ a pair parabolas and see what we can determine about them.1.
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First, we know that this parabola is vertical (opens either up or down) since the x is squared. We have the right to determine it opens up down since the a (-2) is negative.Next we can find the crest (h, k). For a upright parabola, h is inside parenthesis, and since there is a negative in the pattern, we have to take the opposite. Therefore h = -3. K is outside, and also the authorize in the sample is positive, so us will store this number together is. K = 4. Thus, our vertex is (-3, 4).Summary: This is a vertical parabola that opens down. Its vertex is (-3, 4).
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First, we know that this parabola is horizontal (opens one of two people left or right) due to the fact that the y is squared. We have the right to determine it opens to the right due to the fact that the a (1/2) is positive.Next we can find the crest (h, k). For a horizontal parabola, h is outside parenthesis, and since there is a positive in the pattern, we will certainly leave it as is. So h = -1. K is inside, and also the sign in the sample is negative, therefore we will certainly take the opposite. K = 4. Thus, our vertex is (-1, 4).Summary: This is a horizontal parabola that opens to the right. Its vertex is (-1, 4).

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Practice: recognize whether the parabola opens up up, down, left, or right. Then uncover its vertex.1.
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Answers: 1) opens up up, vertex: (-5, -2) 2) opens up to the left, vertex: (-5, 4) 3) opens up to the right, vertex: (6, -3) 4) opens up, vertex: (0, -3) 5) opens up down, vertex: (4, 1)
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