Question

How do you find the vertex of `h(x) + 3/16x^2 - 5/8x - 1/2`?

Answer 1

`x_("vertex")=5/3`

I have left `y_("vertex")` for you to derive by substitution.

Explanation:

Quick method: Find `x_("vertex")` then substitute it back into the original equation to find `y_("vertex")`

Given:`" "3/16 x^2 -5/8 x-1/2` ............................(1)

'~~~~~~~~~~~~ For reference: ~~~~~~~~~~~~~~~~~
`color(brown)(3/16 xxk =5/8) -> color(green)(k=5/8xx16/3= 10/3)`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Write equation (1) as:

`3/16(x^2color(green)(-10/3)x)-1/2`

`color(blue)(x_("vertex")= (-1/2)xx(-10/3) =+ 10/6 = +5/3 = 1.6667)`