Question

Write the standard form of the equation of the parabola vertex (2,3) and point (-1,6) ?

Answer 1

`y=x^2-4x+7`

Explanation:

We have the coordinates of the vertex and a point on the parabola.

Vertex form of a quadratic is given as:

`y=a(x-h)^2+k`

Where:

• `bba = "the coefficient of" color(white)(8)bb(x^2)`
• `bbh = "the axis of symmetry"`
• `bbk = "the maximum/minimum value"`

Note:

The axis of symmetry is the x coordinate of the vertex.

Plugging in known values of the vertex into:

`y=a(x-h)^2+k`

`y=(x-(2))^2+3`

We expand this to get the form:

`bb(y=ax^2+bx+c)`

`y=(x-2)^2+3`

`y=x^2-4x+4+3`

Simplify:

`y=x^2-4x+7`

`:.`

`(x-2)^2+3-=x^2-4x+7`