Question

How is the graph of `g(x)=3/4x^2+5/6` related to the graph of `f(x)=x^2`?

Answer 1

See explanation below

Explanation:

We know that `y=x^2` has a tipical form as follows
graph{x^2 [-10, 10, -5, 5]}
If we apply a factor bigger than 1 the parabola close towards y axis, but if this factor is smaller than 1, the parabola open her branches towards x axis as follows graph{0.05x^2 [-10, 10, -5, 5]}
By the other hand, we know that applying a add number, the parabola moves up if it is poisitive or down if it's negative. So, in our case, `y=3/4x^2+5/6` is a parabola more open than `y=x^2` and displaced 5/6 upwards graph{3/4x^2+5/6 [-10, 10, -5, 5]}