Answer:
f(x) = 2(x –3)²
Step-by-step explanation:
f(x) = 2x² – 12x + 18
The vertex form of the above expression can be obtained as follow:
f(x) = 2x² – 12x + 18
Factorise
f(x) = 2(x² – 6x + 9)
Next, we shall simplify x² – 6x + 9 by factorisation method.
This is illustrated below:
x² – 6x + 9
Multiply the first term i.e x² and last term i.e 9 together. The result is 9x².
Next, find two factors of 9x² such that their sum will result to the 2nd term i.e –6x in the expression above.
The factors are –3x and –3x
Next, replace –6x with –3x and –3x in the equation above as shown below:
x² – 6x + 9
x² – 3x –3x + 9
Factorise
x(x – 3) –3(x –3)
(x –3)(x –3)
(x –3)²
f(x) = 2x² – 12x + 18
f(x) = 2(x² – 6x + 9)
f(x) = 2(x –3)²
Therefore, the vertex form of the function f(x) = 2x² – 12x + 18 is
f(x) = 2(x –3)²
Answer:
1 triangle
Step-by-step explanation:
With three forced sides you can only have 1 triangle as to make it different you would have to change a side length which wouldn't be possible. Where as if it was 3 angles then it would be infinitely many.
