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How are the vertices of the parabolas related to the equation of the quadratic function?
Suppose the equation of the parabola is
y = ax2 + bx + c where a, b, and c are constants, and a ≠0.
The roots of the parabola are given by x = [-b ± sqrt(D)]/2a where D is the discriminant.
Rather than solve explicitly for the coordinates of the vertex, note that the vertical line through the vertex is an axis of symmetry for the parabola. The two roots are symmetrical about x = -b/2a so, whatever the value of D and whether or not the parabola has real roots, the x coordinate of the vertex is -b/2a.
It is simplest to substitute this value for x in the equation of the parabola to find the y-coordinate of the vertex, which is c - b2/2a.
What else can I help you with?
How the quadratic equation is applied in real situation?
Vertices in quadratic equations can be used to determine the highest price to sell a product before losing money again.
Can two parabolas of the form with different vertices have the same axis of symmetry?
The form is not specified in the question so it is hard to tell. But two parabolas with different vertices can certainly have the same axis of symmetry.
What two shapes has 10 faces 16 edges and 16 vertices?
There cannot be such shapes.The Euler characteristic for each shape requires Faces + Vertices = Edges + 2Therefore, for 2 shapes, F + V = E + 4The equation fails in this case.There cannot be such shapes.The Euler characteristic for each shape requires Faces + Vertices = Edges + 2Therefore, for 2 shapes, F + V = E + 4The equation fails in this case.There cannot be such shapes.The Euler characteristic for each shape requires Faces + Vertices = Edges + 2Therefore, for 2 shapes, F + V = E + 4The equation fails in this case.There cannot be such shapes.The Euler characteristic for each shape requires Faces + Vertices = Edges + 2Therefore, for 2 shapes, F + V = E + 4The equation fails in this case.
What is the relationship between faces vertices and edges on a 3D shape?
Their relationship is modelled by the equation F + V = E + 2, where F is the number of faces, V is the number of vertices, and E is the number of edges.
What is the simplest polytope with strictly triangular faces?
A tetrahedron is the simplest polytope with strictly triangular faces. The tetrahedron has six faces and has slightly raised two opposite vertices of the base of a quadratic pyramid.
What is the definition of a Vertex form of a quadratic function?
it is a vertices's form of a function known as Quadratic
How the quadratic equation is applied in real situation?
Vertices in quadratic equations can be used to determine the highest price to sell a product before losing money again.
Can two parabolas of the form with different vertices have the same axis of symmetry?
The form is not specified in the question so it is hard to tell. But two parabolas with different vertices can certainly have the same axis of symmetry.
How do you find the vertices of a cubic function?
A cubic function is a smooth function (differentiable everywhere). It has no vertices anywhere.
What equation coul you write to compare the number of faces to the number of vertices in a rectangular pyramid?
In pyramids, faces equal vertices. 5 = 5
Is an exponential function is the inverse of a logarithmic function?
No, an function only contains a certain amount of vertices; leaving a logarithmic function to NOT be the inverse of an exponential function.
If a polygon has a total of 560 diagonals how many vertices does it have?
The formula to calculate the number of diagonals in a polygon is n(n-3)/2, where n represents the number of vertices. Setting this formula equal to 560 and solving for n, we get n(n-3)/2 = 560. By solving this quadratic equation, we find that the polygon has 20 vertices.
What equation could you write to compare the number of faces to the number of vertices in a rectangular pyramid?
do 4+4=8
What two shapes has 10 faces 16 edges and 16 vertices?
There cannot be such shapes.The Euler characteristic for each shape requires Faces + Vertices = Edges + 2Therefore, for 2 shapes, F + V = E + 4The equation fails in this case.There cannot be such shapes.The Euler characteristic for each shape requires Faces + Vertices = Edges + 2Therefore, for 2 shapes, F + V = E + 4The equation fails in this case.There cannot be such shapes.The Euler characteristic for each shape requires Faces + Vertices = Edges + 2Therefore, for 2 shapes, F + V = E + 4The equation fails in this case.There cannot be such shapes.The Euler characteristic for each shape requires Faces + Vertices = Edges + 2Therefore, for 2 shapes, F + V = E + 4The equation fails in this case.
What is the relationship between faces vertices and edges on a 3D shape?
Their relationship is modelled by the equation F + V = E + 2, where F is the number of faces, V is the number of vertices, and E is the number of edges.
What is the simplest polytope with strictly triangular faces?
A tetrahedron is the simplest polytope with strictly triangular faces. The tetrahedron has six faces and has slightly raised two opposite vertices of the base of a quadratic pyramid.
How many vertices does a heptahedron have?
A heptahedron is a polyhedron with seven faces. The number of vertices in a heptahedron can be determined using Euler's formula, which states that for any polyhedron, the number of vertices (V), edges (E), and faces (F) are related by the equation V - E + F = 2. Since a heptahedron has 7 faces, the equation becomes V - E + 7 = 2. The number of edges in a heptahedron can vary depending on its specific shape, so the number of vertices cannot be determined without additional information about the edges.
