Question

What type of graph is given by `y = ax^2 + bx + c`?

Answer 1

A parabola. A quadratic function is of degree `2`, so will only have one turning point. Thus it will be a parabola, which sort of loos like a stretched out bowl.

For instance, here is `y =x^2`:

graph{x^2 [-10, 10, -5, 5]}

Here is `y = -1/100x^2`

graph{y = -1/100x^2 [-36.5, 36.53, -18.26, 18.25]}

Hopefully this helps!

Answer 2

Always a parabola.

Explanation:

The "mother" function `y=x^2` looks like this:
graph{x^2 [-9.37, 10.63, -1.48, 8.52]}
But even complicated quadratic functions still have the shape of a parabola, like `y=1/4x^2-2x-2`
graph{1/4x^2-2x-2 [-6.78, 25.25, -6.01, 10.02]}
If the number before the `x^2` is negative, the graph will be upside down like `y=-1/4x^2-2x-2`
graph{-1/4x^2-2x-2 [-19.99, 12.04, -12.61, 3.42]}