# Quadratic Function: Opened Upward, Downward

How to find if the graph of a quadratic function is opened upward or downward: formula, 2 examples, and their solutions.

## Formula

For a quadratic function

y = ax^{2} + bx + c,

if a is plus,

then the graph of the function

is opened upward: ∪.

(The graph of a quadratic function

looks like a U shape.

It's called a parabola.)

If a is minus,

then the graph of the function

is opened downward: ∩.

## Exampley = x^{2} + 2x + 5

Solution

Solution (Detail)

The given quadratic function is

y = 1x^{2} + 2x + 5.

a = 1

a is plus.

So the graph of the quadratic function

is opened upward: ∪.

So

opened upward

is the answer.

## Exampley = -3x^{2} + x - 8

Solution

Solution (Detail)

The given quadratic equation is

y = -3x^{2} + x - 8.

a = -3

a is minus.

So the graph of the quadratic function

is opened downward: ∩.

So

opened downward

is the answer.