Find the minimum y-value on the graph of y=f(x)

f(x) = 7x^2 + 7 - 6

The minimum y-value is

 or  

Step-by-step explanation:

we have

This is the equation of a vertical parabola open up

The vertex is the minimum y-value on the graph

Convert the equation into vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

Factor the leading coefficient

Complete the square. Remember to balance the equation by adding the same constants to each side

Rewrite as perfect squares

------> equation in vertex form

The vertex is the point (-0.5,-7.75)

therefore

The minimum is the point (-0.5,-7.75)

The minimum y-value is

see the attached figure to better understand the problem

in the attachment.   i didn't see your choices.   the word which means there is choices.

step-by-step explanation:

(x,y)

x tells you how much left or right you go from the origin

y tells you how much down or up you go from the origin

so for example (-3,2), you go left 3 and up twice. i denoted which of the ordered pairs is which in my graph.