Question

How do you find the vertex of `y=2x^2-10x+3`?

Answer 1

`"vertex "=(5/2,-19/2)`

Explanation:

`"given a parabola in standard form"`

`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)`

`y=2x^2-10x+3" is in standard form"`

`"with "a=2,b=-10" and "c=3`

`x_("vertex")=-(-10)/4=5/2`

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

`y_("vertex")=2(5/2)^2-10(5/2)+3=-19/2`

`color(magenta)"vertex "=(5/2,-19/2)`
graph{2x^2-10x+3 [-20, 20, -10, 10]}