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How do you find an equation of a parabola using the vertex and a point it passes through?
I would use the alternate parabolic equation (y-k)2 = a (x-h). You can plug in the coordinates of the vertex (h, k)--h is the x coordinate of the vertex and k is the y coordinate of the vertex.
Now you are left with an equation with an x and y, which are fine, but also an a, which we still have to get rid of. The a describes how steeply the parabola increases. To find the actual number, plug the other point you were given into the equation (where the x and y are). How you are left with one equation and one variable, so you can solve for a = some number.
Now return to the beginning of the previous step, when you had and x, y, and a in your equation. Keep the x and y in their original positions, but replace a with the number you just found.
What else can I help you with?
What is the equation for the parabola with the vertex -3.0 that passes through the point 318?
To find the equation of a parabola with vertex at ((-3, 0)) that passes through the point ((3, 18)), we can use the vertex form of a parabola, (y = a(x + 3)^2). To determine the value of (a), substitute the point ((3, 18)) into the equation: [ 18 = a(3 + 3)^2 \implies 18 = a(6)^2 \implies 18 = 36a \implies a = \frac{1}{2}. ] Thus, the equation of the parabola is (y = \frac{1}{2}(x + 3)^2).
What is The vertical line passing through the vertex of parabola is called?
The vertical line passing through the vertex of a parabola is called the axis of symmetry. It divides the parabola into two mirror-image halves and is perpendicular to the directrix. The equation of this line can be represented by the x-coordinate of the vertex in the case of a vertically oriented parabola.
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 this parabola is at 3 1 When the y-value is 0 the x-value is 4 What is the coefficient of the squared term in the parabolas equation?
To find the coefficient of the squared term in the parabola's equation, we can use the vertex form of a parabola, which is (y = a(x - h)^2 + k), where ((h, k)) is the vertex. Given the vertex at (3, 1), the equation starts as (y = a(x - 3)^2 + 1). Since the parabola passes through the point (4, 0), we can substitute these values into the equation: (0 = a(4 - 3)^2 + 1), resulting in (0 = a(1) + 1). Solving for (a), we find (a = -1). Thus, the coefficient of the squared term is (-1).
What is the equation of a parabola with the vertex of 2 -1?
3
What is an equation of the parabola in vertex form that passes through (13 8) and has vertex (3 2).?
please help
What is the equation for the parabola with the vertex -3.0 that passes through the point 318?
To find the equation of a parabola with vertex at ((-3, 0)) that passes through the point ((3, 18)), we can use the vertex form of a parabola, (y = a(x + 3)^2). To determine the value of (a), substitute the point ((3, 18)) into the equation: [ 18 = a(3 + 3)^2 \implies 18 = a(6)^2 \implies 18 = 36a \implies a = \frac{1}{2}. ] Thus, the equation of the parabola is (y = \frac{1}{2}(x + 3)^2).
What is the equation of vertex in parabola?
0,0
What is The vertical line passing through the vertex of parabola is called?
The vertical line passing through the vertex of a parabola is called the axis of symmetry. It divides the parabola into two mirror-image halves and is perpendicular to the directrix. The equation of this line can be represented by the x-coordinate of the vertex in the case of a vertically oriented parabola.
The vertex of the parabola below is at the point (-4-2) which equation below could be one for parabola?
-2
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 this parabola is at 3 1 When the y-value is 0 the x-value is 4 What is the coefficient of the squared term in the parabolas equation?
To find the coefficient of the squared term in the parabola's equation, we can use the vertex form of a parabola, which is (y = a(x - h)^2 + k), where ((h, k)) is the vertex. Given the vertex at (3, 1), the equation starts as (y = a(x - 3)^2 + 1). Since the parabola passes through the point (4, 0), we can substitute these values into the equation: (0 = a(4 - 3)^2 + 1), resulting in (0 = a(1) + 1). Solving for (a), we find (a = -1). Thus, the coefficient of the squared term is (-1).
Find equation what parabola its vertex is 0 0 and it passes through point 2 12 express the equation in standard form?
Y=3x^2 and this is in standard form. The vertex form of a prabola is y= a(x-h)2+k The vertex is at (0,0) so we have y=a(x)^2 it goes throug (2,12) so 12=a(2^2)=4a and a=3. Now the parabola is y=3x^2. Check this: It has vertex at (0,0) and the point (2,12) is on the parabola since 12=3x2^2
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.
How do you find the equation of a parabola if you know the vertex and a point it passes through?
Use this form: y= a(x-h)² + k ; plug in the x and y coordinates of the vertex into (h,k) and then the other point coordinates into (x,y) and solve for a.
What is the equation of a parabola with a vertex at 0 0 and a focus at 0 6?
The standard equation for a Parabola with is vertex at the origin (0,0) is, x2 = 4cy if the parabola opens vertically upwards/downwards, or y2 = 4cx when the parabola opens sideways. As the focus is at (0,6) then the focus is vertically above the vertex and we have an upward opening parabola. Note that c is the distance from the vertex to the focus and in this case has a value of 6 (a positive number). The equation is thus, x2 = 4*6y = 24y
What is an equation of the parabola in vertex form that passes through (13 8)(13 8) and has vertex (3 2)(3 2).?
Vertex form is denoted by: y=a(x-h)2+k Where (h,k) is the vertex. So, we have: y=a(x-2)2+3 (This super\subscript thing is annoying). Plug in the values for x and y for the point in the equation and you have your answer.
