Question

What is the vertex form of `y=x^2+14x+3`?

Answer 1

`(x+7)^2=y+46`

Explanation:

Given equation:

`y=x^2+14x+3`

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

`y=(x+7)^2-46`

`(x+7)^2=y+46`

The above equation is in vertex form of upward parabola: `(x-x_1)^2=4a(y-y_1)`

The vertex of parabola :`(x-x_1=0, y-y_1=0)`

`(x+7=0, y+46=0)\equiv(-7, -46)`

Answer 2

`y=(x+7)^2-46`

Explanation:

`"the equation of a parabola in "color(blue)"vertex form"` is.

`•color(white)(x)y=a(x-h)^2+k`

`"where "(h,k)" are the coordinates of the vertex and a"`
`"is a multiplier"`

`"to obtain this form "color(blue)"complete the square"`

`y=x^2+2(7)x+49-49+3`

`y=(x+7)^2-46larrcolor(red)"in vertex form"`