Consider the quadratic function fx2x22x4 Determine the follo

Consider the quadratic function f(x)=2x22x+4.

Determine the following: (enter all numerical answers as integers, fractions, or decimals):

The smallest x-intercept is x=  .
The largest x-intercept is x=  .
The y-intercept is y=  .
The vertex is ( ,  ).
The line of symmetry has the equation  .

Solution

f(x)= 2x2^2x+4.

For X intercept plug f(x) =0

-2x^2 -2x +4 =0

Solve the quadratic: -2x^2 -4x + 2x +4 = -2x( x +2) +2( x+2) =0

(-2x +2)(x+2) =0 --> x = -2 ; x=1

So, Smallest X intercept : x = -2

Largest X intercept x =1

Y intercept : Plug x=0 in f(x) we get :

f(0) = -2(0) +-2(0) +4 =4

Y intercept y=4

Vertex: For a standard quadratic equation ax^2 +bx +c Vertex : (h, k) ; h = -b/2a ; k = f(h)

h = -(-2)/(2*-2) = 2/-4 = -1/2

f(-1/2) = -2(-1/2)^2 -2(-1/2) +4 = -2(1/4) +1 +4 = -1/2 +5 = 9/2

Vertex ( -1/2, 9/2)

Line of symmetry : x= -b/2a ; x= -1/2