Question

draw graph of the function f( x) =- 2 x ^2+ 4 x

Answer 1

Given :

A function f( x) = - 2x² + 4 x

To find :

Graph of the given function

Solution :

•Let f(x) be y

so, y = -2x² + 4x

-y = 2x² - 4x

•Adding 2 both sides

-y + 2 = 2x² - 4x + 2

-y + 2 = 2(x² - 2x + 1)

-(y - 2) = 2( x - 1 )²

( x - 1 )² = -(y - 2)/2

•It is of the form x² = -4ay i.e. it is the equation of Lower parabola

•Parabola is the locus of a point which moves in such a way that its distance from fixed point is equal to distance from fixed line

•Axis of parabola is -ve y axis

•Vertex of parabola is at (1,2)

• Graph of function is drawn .