Help With Proving Quadratic Functions in a Graph

[Ccamm]

I need help just starting off this proof then I should be able to do the rest. The proof is to prove y=ax^2 algebraic, y is the height in the graph and x is the x point of the graph. And a is the fatness of the parabola. The only problem is I'm having difficulty trying to start of this algebraic proof.

[jg.allinsymbols]

Could you use the Distance Formula? The equation for a parabola is derived using the distance formula. You might then use the distance formula again to show that a point on the graph above the horizontal line containing the vertex is the same as the value of the function. This seems redundant.

[stapel_eliz]

The proof is to prove y=ax^2 algebraic, y is the height in the graph and x is the x point of the graph. And a is the fatness of the parabola. The only problem is I'm having difficulty trying to start of this algebraic proof.

What does your book (or instructor) mean by proving that "y = ax^2" is "algebraic"?

[jg.allinsymbols]

I need help just starting off this proof then I should be able to do the rest. The proof is to prove y=ax^2 algebraic, y is the height in the graph and x is the x point of the graph. And a is the fatness of the parabola. The only problem is I'm having difficulty trying to start of this algebraic proof.

What is the exact problem description, word-for-word? Is a picture, graph, or diagram included?