Question

How do you find the vertex and intercepts for `f(x) = 2x^2 - 4x + 3`?

Answer 1

`"see explanation"`

Explanation:

`"express the quadratic in "color(blue)"vertex form"`

`•color(white)(x)y=a(x-h)^2+k`

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

`"using the method of "color(blue)"completing the square"`

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

`color(white)(f(x))=2(x^2+2(-1)x+1-1+3/2)`

`color(white)(f(x))=2(x-1)^2+1`

`"vertex "=(1,1)`

`"for y-intercept set x = 0"`

`f(0)=3rArr(0,9)`

`"for x-intercepts set y = 0"`

`2(x-1)^2+1=0`

`(x-1)^2=-1/2`

`"this has no real solutions hence no x-intercepts"`
graph{2x^2-4x+3 [-10, 10, -5, 5]}