Algebra II/Parabola
A parabola is an approximate u-shaped curve in which any point is equidistant from the focus (fixed point) and the directrix (fixed straight line). The standard form of the parabola is ^{2} . The vertex is found by taking the opposite of the "h" and taking the "k": . The axis of symmetry is (opposite of h).
For example:
- ^{2}
Vertex: (3, -7)
Axis of Symmetry: x = 3
Positive or negative?: The "4" in this equation represents whether the graph is going up (positive) or is negative (down). In this case, since we have a positive "4", it is going up (and therefore, positive).
Here are a few tricky ones:
- ^{2}
Vertex: (-1, 0) [no presence of a "k", so therefore, a zero takes its place]
Axis of Symmetry: x = -1
Positive or negative?: Negative
- ^{2} - 7
Vertex: (0, -7) [no presence of a "h", so therefore, a zero takes its place]
Axis of Symmetry: x = 0
Positive or negative?: Negative
- ^{2}
Vertex: (0, 0)
Axis of Symmetry: x = 0 [no presence of a "h", so therefore, a zero takes its place]
Positive or negative?: Positive
Quadratic Function → Standard Form [Parabola Equation]
edit- ^{2}
- Bring the "5" to the other side, or the "c" (constant term).
- ^{2}
- Divide the "4", or the "bx" (linear term), by "2". Then square it and add it to both sides.
- ^{2}
- Bring the constant term to the other side.
- ^{2}
- You're finished. This is your answer--now you can figure out the vertex and the AOS. The vertex for this problem is (2, 1) and the AOS is x = 2.
- ^{2}
- Bring the constant term to the other side
- ^{2}
- Break down " ^{2} "
- ^{2}
- Divide the linear team by 2, then square that number, multiply the number by "2" (the 2 infront of the paranthesis) and add it on both sides.
- ^{2}
- Break down " ^{2} ".
- ^{2}
- Move the "37" to the other side. Your problem is finished!
- ^{2}
- The vertex is (-4, -37), the AOS is x = -4 and the parabola here is positive due to the positive "2".