Given the function fx2x27x4 write your answers from the smal

Given the function f(x)=2x^2-7x-4 (write your answers from the smallest to the largest numbers) (a) If x = 2 what is the value of f(x) ? f(x) = What point is on the graph? (b) Is the point (1, -9) on the graph ? (c) If f(x) = -4 what is x ? x= , x= What point(s) is on the graph? (d) Find x-intercepts. x = , x= (e) Find y-intercept. y= (f) What is the domain?

Solution

Answer:

Given the function f(x)=2x^2-7x-4

( a ) If x = 2 then the value of f(x) is f(2) = 2(2)^2-7(2)-4 = -10

( b ) if x =1 then f(1) = 2(1)^2-7(1)-4 = -9

Therefore ( 1 , - 9 ) is on the graph of the function f(x)=2x^2-7x-4

( c ) If f( x ) = -4 then 2x^2-7x-4 = -4

                                 2x^2-7x =0

                                 x(2x - 7) = 0

                                 x = 0 or 2x - 7= 0 implies that x = 7/2

Both the points ( 0 , -4 ) and ( 7/2 , -4 ) are on the point.

(d) To find the x-intercept let y = 0 and solve for x.

That is 2x^2 - 7x - 4 =0

          2x^2 - 8x + x - 4 = 0

          2x( x - 4 ) + (1)( x - 4) = 0

          ( 2x + 1 )( x - 4 ) = 0

          x - 4 = 0 or 2x + 1 =0

         x = 4 or x = -1/2

Therefore the x- intercepts are ( 4 , 0 ) and ( -1/2 , 0)

( e ) To find the y -intercept let x = 0 then f( 0 ) = 2( 0 )^2 - 7( 0 ) - 4 = - 4

Therefore the y - intercept is ( 0 , - 4 )

( f ) The domain of f(x)=2x^2-7x-4 is ( - infinity , infinity )