Which is the graph of the function f(x)=1/2x^2+2x-6

Step-by-step explanation:

This function could be rewritten as

f(x)=1/2x^2+2x-6 = (1/2)(x^2 + 4x - 3), or

                        f(x) = (1/2)(x + 4)(x - 3)

Setting each factor equal to zero and solving for x results in {-4, 3}, and so the x-intercepts are (x + 4) and (x - 3).

The y-intercept is at f(0) = -6  =>  (0, -6)

The axis of symmetry of this function is x = -4/2 = -2, or x = -2

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)