Question

How do you find the y intercept, axis of symmetry and the vertex to graph the function `f(x)=x^2+12x+36`?

Answer 1

`"see explanation"`

Explanation:

`"factorising f(x) gives"`

`f(x)=(x+6)^2`

`"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 constant.

`y=(x+6)^2+0" is in this form"`

`rArrcolor(magenta)"vertex "=(-6,0)`

`"the axis of symmetry passes through the vertex , is vertical"`
`"with equation "`

`"axis of symmetry is "x=-6`

`"to find y-intercept set x = 0 in the equation"`

`y=(0+6)^2=36larrcolor(red)" y-intercept"`