Question

How do you find the vertex and the intercepts for `y = -4x^2 + 16x - 3`?

Answer 1

Vertex is `(2,13)`

Explanation:

The vertex of the parabola will be the at he maximum of the

function,i.e, where `dy/dx=0.`

`dy/dx=-8x+16=0`

`=>x=2`
The corresponding value of `y` is `13`

The `y`-intercept will be where `x=0` and the `x`-intercept will be where `y=0`

So, `y`-intercept `=-3`
x-intercept is the solution of the equation

`" "-4x^2+16x-3=0`

which by solving we get `x=0.197` and `x=3.803` , these are the `x`-intercepts.
graph{-4x^2+16x-3 [-10.82, 21.23, -0.42, 15.6]}
All these can be checked from the graph of the function

.