The function f is defined by f(x) = -2x^2 + 5x. What is the value of… Step by Step

Step by step

The question

Question: find f(3) for f(x) = −2x² + 5x.

f(x) = −2x² + 5x

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

There are four choices.

First we solve it, the normal way.

Then we pick.

1 Put the number in

f(3) means: put 3 in place of every x.

We write it in brackets: 5x becomes 5 times 3, not 53.

f(3) = −2(3)² + 5(3)

2 Powers

Everyone uses the same order, so we all get the same answer.

Powers come before times and plus.

Order: Powers → × ÷ → + −

3² means 3 times 3.

3² = 3 × 3

= 9

That is 9.

= −2(9) + 5(3)

3 Times and divide

Times comes before plus.

−2(9) means −2 times 9.

9 has no sign, so it is plus.

Minus times plus is minus.

−2(9) = −2 × 9

− × + = −

2 times 9 is 18.

So we get −18.

= −18 + 5(3)

Times comes before plus.

5(3) means 5 times 3.

5(3) = 5 × 3

5 times 3 is 15.

= −18 + 15

4 Plus and minus

−18 is 18 below 0.

15 is not enough to reach 0.

We stay 18 − 15 = 3 below 0.

18 − 15 = 3

We land on −3.

f(3) = −3

So f(3) = −3.

5 Pick the choice

Our answer is f(3) = −3.

That is choice B.

B) −3

6 Why not the others

A is −33.

Wrong: 5 × 3 is +15, not −15.

A) −33 ✗ 5 × 3 is +15, not −15

C is 33.

Wrong: lost the minus: −2 × 9 is −18.

C) 33 ✗ lost the minus: −2 × 9 is −18

D is 51.

Wrong: squared −2 × 3: only the x is squared.

D) 51 ✗ squared −2 × 3: only the x is squared

Let's look back.

First: put the number in.

Then: powers.

Then: times and divide.

Then: plus and minus.

Then: pick the choice.

Last: why not the others.

Answer