Question

Identify the vertex, and the Y-intercept then click another point of parabola

Answer 1

Given equation of a parabola is,

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

To find the vertex of the parabola.

we know that,

Equation of the parabola is,

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

where (h,k) is the vertex of the parabola.

we know that f(x)=y, the equation becomes,

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

To rewrite the above equation in the required format, adding and subtracting by1, we get

`y=x^2-2x+1-1+3`
`y=(x-1)^2+2`

we get the vertex as (1,2)

Vertex is (1,2)

y-intercept:

when x=0, we get y=3

y-intercept is y=3.

Answer is:

Vertex is (1,2) an y-intercept is y=3.