Menu Close

What is the equation of the parabola in vertex form with vertex at 2 4?

Admin

What is the equation of the parabola in vertex form with vertex at 2 4?

Explanation: Standard equation of a vertical parabola with vertex (h,k) is (x−h)2=4p(y−k) where p is the distance of the focus from the vertex. In the present case vertex is (2,4).

How do you write an equation in vertex form with the vertex and a point?

  1. Vertex form of a quadratic equation is y=a(x-h)2+k, where (h,k) is the vertex of the parabola.
  2. The vertex of a parabola is the point at the top or bottom of the parabola.
  3. ‘h’ is -6, the first coordinate in the vertex.
  4. ‘k’ is -4, the second coordinate in the vertex.
  5. ‘x’ is -2, the first coordinate in the other point.

How do you find the vertex form?

To find the vertex of a parabola in standard form, first, convert it to the vertex form y=a(x−h)2+k y = a ( x − h ) 2 + k .

What is vertex form of a parabola?

Vertex Form of Equation The vertex form of a parabola’s equation is generally expressed as: y = a(x-h)2+k. (h,k) is the vertex as you can see in the picture below. If a is positive then the parabola opens upwards like a regular “U”. If a is negative, then the graph opens downwards like an upside down “U”.

What is a parabola in vertex form?

The vertex form of a parabola’s equation is generally expressed as: y = a(x-h)2+k. (h,k) is the vertex as you can see in the picture below. If a is positive then the parabola opens upwards like a regular “U”. If a is negative, then the graph opens downwards like an upside down “U”.

How do I find the vertex of a parabola?

y=ax2+bx+c . In this equation, the vertex of the parabola is the point (h,k) . You can see how this relates to the standard equation by multiplying it out: y=a(x−h)(x−h)+ky=ax2−2ahx+ah2+k .

What is the vertex in a quadratic equation?

vertex: The point at which a parabola changes direction, corresponding to the minimum or maximum value of the quadratic function.

How do you write a parabola equation in standard form?

For parabolas that open either up or down, the standard form equation is (x – h)^2 = 4p(y – k). For parabolas that open sideways, the standard form equation is (y – k)^2 = 4p(x – h). The vertex or tip of our parabola is given by the point (h, k).