Question

What is the the vertex of `y = (x -4)^2+4x-20`?

Answer 1

`2,-8)`

Explanation:

`"given a quadratic in "color(blue)"standard form"`

`•color(white)(x)y=ax^2+bx+c color(white)(x);a!=0`

`"then the x-coordinate of the vertex is"`

`•color(white)(x)x_(color(red)"vertex")=-b/(2a)`

`"expand and rearrange into this form"`

`y=x^2-8x+16+4x-20`

`color(white)(y)=x^2-4x-4larrcolor(blue)"in standard form"`

`"with "a=1,b=-4" and "c=-4`

`x_("vertex")=-(-4)/2=2`

`"substitute this value into the equation for y"`

`y_("vertex")=(2)^2-4(2)-4=-8`

`color(magenta)"vertex "=(2,-8)`
graph{(x-4)^2-4x-4 [-80, 80, -40, 40]}