Answer: C
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (2, - 4) , thus
y = a(x - 2)² - 4
To find a substitute (3, - 1 ) into the equation
- 1 = a(3 - 2)² - 4 ( add 4 to both sides )
3 = a
Thus
y = 3(x - 2)2 - 4 ← equation in vertex form
= 3(x² - 4x + 4) + 4
= 3x² - 12x + 12 + 4
= 3x² - 12x + 16 ← equation in standard form
with coefficient of x² term = 3
Answer:
B) {
}
Step-by-step explanation:
A function cannot have replicated x-coordinates. All the other answer choices do, so you would pick this one.
I am joyous to assist you anytime.
Answer:
Consider the following calculations
Step-by-step explanation:
Since 1 Blimp uses 2 components of B and C each
=> choosing 2 components of B(remaining after using in other prototypes) for 1st model= 22C2
choosing 2 components of B(remaining after using in other prototypes) for 2nd model= 21C2
choosing 2 components of B(remaining after using in other prototypes) for 3rd model= 20C2
choosing 2 components of B(remaining after using in other prototypes) for 4th model= 19C2
choosing 2 components of B(remaining after using in other prototypes) for 5th model= 18C2
and choosing 2 components of C(remaining after using in other prototypes) = 24C2
Similarly for C
P(5 prototypes of Blimp created)=[(22C2 / 25C2 )*(24C2 / 25C2 )] + [(21C2 / 25C2 )*(23C2 / 25C2 )]+[(20C2 / 25C2 )*(22C2 / 25C2 )]+[(19C2 / 25C2 )*(21C2 / 25C2 )]+[(18C2 / 25C2 )*(20C2 / 25C2 )]
The graph of the function

is parabola with branches going down in the negative direction of y-axis.
The vertex of parabola has coordinates:

Then you can conclude that all x are possible, that means that the dimain is

and the maximum value of y is at the vertex, then the range is
![(-\infty,6]](https://tex.z-dn.net/?f=%28-%5Cinfty%2C6%5D)
.The function is increasing for x<-2 and decreasing for x>-2 (since vertex is the maximum point).
When x=0, y=2.
Hence,
<span>The domain is {x|x ≤ –2} - false.
</span>
<span>The range is {y|y ≤ 6} - true.
</span>
<span>The function is increasing over the interval (–∞ , –2) - true.
</span>
<span>The function is decreasing over the interval (−4, ∞) - false.
</span>
<span>The function has a positive y-intercept - true.</span>