Name: Evaluating a function at an expression: solution walkthrough
Uploaded: 2026-11-13
Duration: 1 min 55 s
Description: If f(x) = x² - 3x + 5, which of the following expressions is equal to f(a + 1)? Try it, then watch the animated solution.

The input is the whole expression

a + 1

. It takes the place of every

x

in the rule.

Replace each

x

with

(a + 1)

in parentheses:

f(a + 1) = (a + 1)^2 - 3(a + 1) + 5

.

(a + 1)^2 = (a + 1)(a + 1) = a^2 + 2a + 1

. A square with side

a + 1

has four pieces.

Multiply both terms by

{-3}

:

{-3}(a + 1) = {-3}a - 3

.

Combine like terms:

2a - 3a = -a

and

1 - 3 + 5 = 3

. So

f(a + 1) = a^2 - a + 3

.

Traps: adding the

1

at the end, losing the

2a

from the square, or multiplying only

a

by

{-3}

.

Try it first