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Parabola finding vertex and X intercepts
Vertex and X-Intercept of a Parabola
Parabolas have a highest or a lowest point, known as their vertex, which represents its turning point on a graph. If a parabola opens upward, its vertex is the lowest point on the graph, or absolute minimum. If it opens downward, its vertex is the highest point, or absolute maximum. Each parabola has a vertical line or axis of symmetry that passes through its vertex. Because of this symmetry, the axis passes through the midpoint of the two x-intercepts (roots or solutions) of the parabola. That is, if the parabola does indeed have two real solutions.
The general form of a parabola’s equation is
The vertex form a parabola’s equation is
If the leading coefficient a is greater than 0, the parabola will open upward. If a is less than 0, the parabola will open downward.
For any parabola given in the general form of , the x-coordinate of the vertex is given by .
To determine the y-intercept, use the general form and set .
The vertex is apparent (h, k) in the vertex form.
Parabolas can model many real life situations, such as the height above ground of an object traveling upward for some period of time. The vertex of the parabola can provide us with information, for example, about the maximum height reachable by the upward traveling object. This is one reason we might want to be able to find the coordinates of the vertex.
Parabolas have a highest or a lowest point, known as their vertex, which represents its turning point on a graph. If a parabola opens upward, its vertex is the lowest point on the graph, or absolute minimum. If it opens downward, its vertex is the highest point, or absolute maximum. Each parabola has a vertical line or axis of symmetry that passes through its vertex. Because of this symmetry, the axis passes through the midpoint of the two x-intercepts (roots or solutions) of the parabola. That is, if the parabola does indeed have two real solutions.
The general form of a parabola’s equation is
The vertex form a parabola’s equation is
If the leading coefficient a is greater than 0, the parabola will open upward. If a is less than 0, the parabola will open downward.
For any parabola given in the general form of , the x-coordinate of the vertex is given by .
To determine the y-intercept, use the general form and set .
The vertex is apparent (h, k) in the vertex form.
Parabolas can model many real life situations, such as the height above ground of an object traveling upward for some period of time. The vertex of the parabola can provide us with information, for example, about the maximum height reachable by the upward traveling object. This is one reason we might want to be able to find the coordinates of the vertex.