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How does an equation for a sideways parabola look like?
An equation for a sideways parabola can be expressed in the form ( y^2 = 4px ) for a parabola that opens to the right, or ( y^2 = -4px ) for one that opens to the left. Here, ( p ) represents the distance from the vertex to the focus. The vertex of the parabola is at the origin (0,0), and the axis of symmetry is horizontal. If the vertex is not at the origin, the equation can be adjusted to ( (y-k)^2 = 4p(x-h) ), where ((h, k)) is the vertex.
What is a quadratic equation in vertex form for a parabola with vertex (11 -6)?
A quadratic equation in vertex form is expressed as ( y = a(x - h)^2 + k ), where ((h, k)) is the vertex of the parabola. For a parabola with vertex at ((11, -6)), the equation becomes ( y = a(x - 11)^2 - 6 ). The value of (a) determines the direction and width of the parabola. Without additional information about the parabola's shape, (a) can be any non-zero constant.
What is the focus of the parabola y equals 4x2?
The equation ( y = 4x^2 ) represents a parabola that opens upwards. To find the focus, we can rewrite it in the standard form ( y = 4p(x - h)^2 + k ), where ( (h, k) ) is the vertex and ( p ) is the distance from the vertex to the focus. Here, the vertex is at the origin ( (0, 0) ) and ( 4p = 4 ), so ( p = 1 ). Thus, the focus of the parabola is located at the point ( (0, 1) ).
What is the equation of a parabola with the vertex of 2 -1?
3
What equation describes a parabola that opens left or right and whose vertex is at the point h v?
The equation of a parabola that opens left or right with its vertex at the point ((h, v)) is given by ((y - v)^2 = 4p(x - h)), where (p) is the distance from the vertex to the focus. If (p > 0), the parabola opens to the right, and if (p < 0), it opens to the left.
How does an equation for a sideways parabola look like?
An equation for a sideways parabola can be expressed in the form ( y^2 = 4px ) for a parabola that opens to the right, or ( y^2 = -4px ) for one that opens to the left. Here, ( p ) represents the distance from the vertex to the focus. The vertex of the parabola is at the origin (0,0), and the axis of symmetry is horizontal. If the vertex is not at the origin, the equation can be adjusted to ( (y-k)^2 = 4p(x-h) ), where ((h, k)) is the vertex.
What is a quadratic equation in vertex form for a parabola with vertex (11 -6)?
A quadratic equation in vertex form is expressed as ( y = a(x - h)^2 + k ), where ((h, k)) is the vertex of the parabola. For a parabola with vertex at ((11, -6)), the equation becomes ( y = a(x - 11)^2 - 6 ). The value of (a) determines the direction and width of the parabola. Without additional information about the parabola's shape, (a) can be any non-zero constant.
The vertex of the parabola below is at the point (-4-2) which equation below could be one for parabola?
-2
The vertex of this parabola is at -2 -3 When the y-value is -2 the x-value is -5 What is the coefficient of the squared term in the parabola's equation?
The vertex of this parabola is at -2 -3 When the y-value is -2 the x-value is -5. The coefficient of the squared term in the parabola's equation is -3.
What is the focus of the parabola y equals 4x2?
The equation ( y = 4x^2 ) represents a parabola that opens upwards. To find the focus, we can rewrite it in the standard form ( y = 4p(x - h)^2 + k ), where ( (h, k) ) is the vertex and ( p ) is the distance from the vertex to the focus. Here, the vertex is at the origin ( (0, 0) ) and ( 4p = 4 ), so ( p = 1 ). Thus, the focus of the parabola is located at the point ( (0, 1) ).
The vertex of the parabola below is at the point 4 -1 which equation be this parabola's equation?
5
The vertex of the parabola below is at the point -3 -5 Which of the equations below could be the equation of this parabola?
2
What is the equation of a parabola with the vertex of 2 -1?
3
What equation describes a parabola that opens left or right and whose vertex is at the point h v?
The equation of a parabola that opens left or right with its vertex at the point ((h, v)) is given by ((y - v)^2 = 4p(x - h)), where (p) is the distance from the vertex to the focus. If (p > 0), the parabola opens to the right, and if (p < 0), it opens to the left.
The vertex of the parabola below is at the point (5 -3). Which of the equations below could be the one for this parabolaus anything?
To determine the equation of a parabola with a vertex at the point (5, -3), we can use the vertex form of a parabola's equation: (y = a(x - h)^2 + k), where (h, k) is the vertex. Substituting in the vertex coordinates, we have (y = a(x - 5)^2 - 3). The value of "a" will determine the direction and width of the parabola, but any equation in this form with varying "a" values could represent the parabola.
What is the focus of the parabola y 4x2?
The equation of the parabola ( y = 4x^2 ) can be rewritten in the standard form ( y = 4p(x - h)^2 + k ), where ( (h, k) ) is the vertex. Here, it is clear that the vertex is at the origin (0, 0) and ( 4p = 4 ), giving ( p = 1 ). The focus of the parabola is located at ( (h, k + p) ), so the focus is at the point ( (0, 1) ).
What is the equation of a parabola with vertex at 1 -3 and focus at 2 -3?
For a parabola with an axis of symmetry parallel to the x-axis, the equation of a parabola is given by: (y - k)² = 4p(x - h) Where the vertex is at (h, k), and the distance between the focus and the vertex is p (which can be calculated as p = x_focus - x_vertex). For the parabola with vertex (1, -3) and focus (2, -3) this gives: h = 1 k = -3 p = 2 - 1 = 1 → parabola is: (y - -3)² = 4×1(x - 1) → (y + 3)² = 4(x - 1) This can be expanded to: 4x = y² + 6y + 13 or x = (1/4)y² + (3/2)y + (13/4)
