Question

What attribute(s) of the graph of a parabola can you IMMEDIATELY (without any work) find given the standard form of a quadratic function? Select all that apply.

a. Vertex
b. Axis of Symmetry/Line of Symmetry
c. Direction of opening (opens up or down)
d. x-intercept(s)
e. y-intercept
f. Domain
g. Range
h. Slope
i. None of the above

Answer 1

c. Direction of opening (opens up or down).

f. Domain.

Explanation:

The standard form of a quadratic function is

`ax^(2) +bx+c=0`

Using this form we can obtaing the values of each coefficient. Specifically, we can know without any work if the parabola opens upside or downside. However, that's the only characteristic we can deduct with just seeing the quadratic function in general form.

Additionally, with the standard form we can also know the domain of the function, which is always all real numbers.

On the other hand, the vertex form of a quadratic function is

`y=a(x-h)^(2) +k`

Using this form, we can deduct the vertex of the parabola and its direction of opening.

Therefore, using only the standard form, we can deduct (without any work) the direction of opening, if opens up or down, and the domain.