Question

What is the graph of `f(x)=-2x^2+7x+4`?

Answer 1

check the explanation below.

Explanation:

`y=-2x^2+7x+4`

Take -2 as a common factor from the first two terms and complete the square afterwards

`y=-2(x^2-7/2x)+4`

`y=-2((x-7/4)^2-(7/4)^2)+4`

`y=-2(x-7/4)^2+10.125`

it's vertex is `(7/4,10.125)`

auxiliary points:

It's intersection with the `x-"axis"`

and opened downwards since the coefficient of `x^2` is negative

`y=0rarr x=-0.5 or x=4`

graph{y=-2x^2+7x+4 [-11.56, 13.76, -1.42, 11.24]}