Write each function in standard form . F(x)= 4(x+1)² -3

The correct answer is: f(x) =0.1x2 -0.4x + 0.3

Hint :- The standard quadratic form is ax²+bx+c=y, the vertex form of a quadratic equation is y=a(x−h)²+k.
Solution :- We have given the function in Vertex form , we have to convert it into standard form.
                      F(x)= 4(x+1)² -3
On further solving this function we will get
F(x) = 4 ( x² + 2x + 1 ) – 3
= 4x² + 8x + 4 – 3
= 4x² + 8x + 1
Therefore, the standard form of given function is f(x) = 4x² + 8x + 1.
                                   
Q39:
Complex Level : Hard
Blooms Level: Understanding
Write each function in standard form . F(x)= 0.1 (x-2)² – 0.1
Hint :- The standard quadratic form is ax²+bx+c=y, the vertex form of a quadratic equation is y=a(x−h)²+k.
Solution :- We have given the function in Vertex form , we have to convert it into standard form.
F(x)= 0.1(x-2)² - 0.1
On further solving this function we will get
F(x) = 0.1 ( x² - 4x + 4 ) – 0.1
= 0.1x² – 0.4x + 0.4 – 0.1
= 0.1x² -0.4x + 0.3
Therefore, the standard form of given function is f(x) =0.1x² -0.4x + 0.3.