Suppose f (x) =x^2 find the graph of f (x+4

The graph in the attached figure

Step-by-step explanation:

we have

To find f(x+4)

substitute the variable (x+4) in the function f(x)

Let

g(x)=f(x+4)

so

The rule of the transformation of f(x) to g(x) is

(x,y) -----> (x-4,y)

The translation is 4 units to the left

using a graphing tool

see the attached figure

Step-by-step explanation:

f(x)  = 2x² + 14x - 4

= 2(x² + 7x) - 4

= 2(x² +7x + 3.5²) - 2(3.5²) - 4

= 2(x+3.5)² - 28.5

vertex (3.5, -28.5) = (7/2, -57/2)

The vertical intercept is the y-intercept, i.e., f(0) = -4.

The x-intercepts are the values of x for which y=0.

2x² + 14x - 4  = 0

x = [-14±√(14²-4(2)(-4))]/[2(2)] = [-7±√57]/2 ≅ -7.27, 0.27