Solve f(x) = 2x^2 - 3x + 1, f(-2) Step by Step

Step by step

The question

Question: find f(−2) for f(x) = 2x² − 3x + 1.

f(x) = 2x² − 3x + 1

f(x) is read "f of x".

It is a rule, called a function.

A number goes in for x.

The rule gives one answer out.

f(x) = "f of x"

x goes in → an answer comes out

1 Put the number in

f(−2) means: put −2 in place of every x.

We write it in brackets.

The brackets keep the minus with the number.

f(−2) = 2(−2)² − 3(−2) + 1

2 Powers

Powers come before times, minus and plus.

Order: ( ) → x² √ → × ÷ → + −

(−2)² means −2 times −2.

Minus times minus is plus.

(−2)² = (−2) × (−2) = 4

That is 4.

= 2(4) − 3(−2) + 1

3 Times and divide

Times comes before minus and plus.

Times and divide: we go from left to right.

same kind: left → right

2(4) = 2 × 4

2(4) means 2 times 4.

2 times 4 is 8.

= 8 − 3(−2) + 1

Times comes before minus and plus.

3(−2) = 3 × (−2)

+ × − = −

3(−2) means 3 times −2.

Plus times minus is minus.

3 times 2 is 6.

So we get −6.

= 8 − (−6) + 1

4 Plus and minus

Plus and minus: we go from left to right.

Taking away a negative is the same as adding.

same kind: left → right

− (−) = +

So 8 − (−6) becomes 8 + 6.

= 8 + 6 + 1

8 plus 6 is 14.

= 14 + 1

14 plus 1 is 15.

f(−2) = 15

So f(−2) = 15.

Let's look back.

First: put the number in.

Then: powers.

Then: times and divide.

Last: plus and minus.

Answer