Answer:
- 5(x +1.5)^2
- 10(x +1)^2
- 1/4(x +2)^2
- 3(x +5/6)^2
Step-by-step explanation:
When your desired form is expanded, it becomes ...
a(x +b)^2 = a(x^2 +2bx +b^2) = ax^2 +2abx +ab^2
This tells you the overall factor (a) is the leading coefficient of the given trinomial. Factoring that out, you can find b as the root of the remaining constant.
a) 5x^2 +15x +11.25 = 5(x^2 +3x +2.25) = 5(x +1.5)^2
b) 10x^2 +20x +10 = 10(x^2 +2x +1) = 10(x +1)^2
c) 1/4x^2 +x +1 = 1/4(x^2 +4x +4) = 1/4(x +2)^2
d) 3x^2 +5x +25/12 = 3(x^2 +5/3x +25/36) = 3(x +5/6)^2
_____
<em>Additional comment</em>
If you know beforehand that the expressions can be factored this way, finding the two constants (a, b) is an almost trivial exercise. It gets trickier when you're trying to write a general expression in vertex form (this form with an added constant). For that, you must develop the value of b from the coefficient of the linear term inside parentheses.
G(x) = 3x + 4
g(-4) = 3(-4) + 4
g(-4) = -12 + 4
g(-4) = -8
Answer:
Step-by-step explanation:
1) 8.9
2) 27.8
3) 24.3
4) 11.4
5) 27.5
6) 49.2
7) 8.1
8)4.8
Answer:
12x+4
Step-by-step explanation:
Use the given functions to set up and simplify (
f
+
g
)
(
x
)
Answer: Your answer is<u> 3.53</u> as a Decimal.
Hope this helps!
