Answer:
f(x) = (x + 1)² + 2 in vertex form ⇒ 3rd answer
Step-by-step explanation:
* Lets revise how to find the vertex form the standard form
- Standard form ⇒ x² + bx + c, where a , b , c are constant
- Vertex form ⇒(x - h)² + k, where h , k are constant and (h , k) is the
vertex point (minimum or maximum) of the function
- At first we must find h and k
- By equating the two forms we can find the value of h and k
* Lets solve the problem
∵ f(x) = x² + 2x + 3 ⇒ standard form
∵ f(x) = (x - h)² + k ⇒ vertex form
- Put them equal each other
∴ x² + 2x + 3 = (x - h)² + k ⇒ open the bracket power 2
∴ x² + 2x + 3 = x² - 2hx + h² + k
- Now compare the like terms in both sides
∵ 2x = -2hx ⇒ cancel x from both sides
∴ 2 = -2h ⇒ divide both sides by -2
∴ -1 = h
∴ The value of h is -1
∵ 3 = h² + k
- Substitute the value of h
∴ 3 = (-1)² + k
∴ 3 = 1 + k ⇒ subtract 1 from both sides
∴ 2 = k
∴ The value of k = 2
- Lets substitute the value of h and k in the vertex form
∴ f(x) = (x - -1)² + 2
∴ f(x) = (x + 1)² + 2
* f(x) = (x + 1)² + 2 in vertex form
