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

Formula

For a quadratic function
y = ax2 + 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.

Example 1

Example

Solution

The given quadratic function is
y = 1x2 + 2x + 5.

a = 1
a is plus.

So the graph of the quadratic function
is opened upward.

So [opened upward] is the answer.

Example 2

Example

Solution

The given quadratic equation is
y = -3x2 + x - 8.

a = -3
a is minus.

So the graph of the quadratic function
is opened downward.

So [opened downward] is the answer.