Write in Standard Form f(x)=3(x+3)^2-25

$f (x) = 3 {(x + 3)}^{2} - 25$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$f (x) = a x^{2} + b x + c$

Step 2

Simplify each term.

Rewrite ${(x + 3)}^{2}$ as $(x + 3) (x + 3)$ .

$f (x) = 3 ((x + 3) (x + 3)) - 25$

Expand $(x + 3) (x + 3)$ using the FOIL Method.

Apply the distributive property.

$f (x) = 3 (x (x + 3) + 3 (x + 3)) - 25$

Apply the distributive property.

$f (x) = 3 (x \cdot x + x \cdot 3 + 3 (x + 3)) - 25$

Apply the distributive property.

$f (x) = 3 (x \cdot x + x \cdot 3 + 3 x + 3 \cdot 3) - 25$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$f (x) = 3 (x^{2} + x \cdot 3 + 3 x + 3 \cdot 3) - 25$

Move $3$ to the left of $x$ .

$f (x) = 3 (x^{2} + 3 \cdot x + 3 x + 3 \cdot 3) - 25$

Multiply $3$ by $3$ .

$f (x) = 3 (x^{2} + 3 x + 3 x + 9) - 25$

Add $3 x$ and $3 x$ .

$f (x) = 3 (x^{2} + 6 x + 9) - 25$

Apply the distributive property.

$f (x) = 3 x^{2} + 3 (6 x) + 3 \cdot 9 - 25$

Simplify.

Multiply $6$ by $3$ .

$f (x) = 3 x^{2} + 18 x + 3 \cdot 9 - 25$

Multiply $3$ by $9$ .

$f (x) = 3 x^{2} + 18 x + 27 - 25$

Step 3

Subtract $25$ from $27$ .

$f (x) = 3 x^{2} + 18 x + 2$