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

1 Answer
Jun 28, 2018

Answer:

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]}