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>
Answer:
Step-by-step explanation:
<u>Given </u><u>:</u><u>-</u><u> </u>
- A quadratic equation is given to us.
- The equation is 2x² + 7x +6=0
And we need to find out the roots of the given equation. We can use the middle term splitting method to find out the roots as ,
<u>Given </u><u>equation</u><u> </u><u>:</u><u>-</u>
Step 1: <u>Find</u><u> out</u><u> the</u><u> </u><u>factors</u><u> </u><u>of </u><u>1</u><u>2</u><u> </u><u>:</u><u>-</u><u> </u>
We will choose the two factors such that their sum equals to the coefficient of x i.e. 7 .The factors are , 1×12 , 2×6 , 3×4 .
- And 3 + 4 = 7. So we will break the middle term into 3x and 4x .
Step 2 :<u> Breaking</u><u> the</u><u> </u><u>middle</u><u> term</u><u> </u><u>:</u><u>-</u><u> </u>
Step 3: <u>Take </u><u>out </u><u>common</u><u> </u><u>from </u><u>terms </u><u>:</u><u>-</u>
Step 4 : <u>Equate </u><u>them </u><u>with </u><u>0</u><u> </u><u>:</u><u>-</u><u> </u>
<u>Hence </u><u>the</u><u> </u><u>correct</u><u> </u><u>options </u><u>are </u><u>C </u><u>and </u><u>D </u><u>.</u>
Answer:
Any number other than 2
Step-by-step explanation:
Well if we plug in any number other than 2 like 1 for the blank and distribute,
the right side becomes,
3x + 6 = 3x + a number other than 6
Parallel lines have the same slope but different y intercept.
Look at the image below ↓
<em>Thus,</em>
<em>to make the equation have no solution the blank has to be any number other than 2.</em>
<em />
<em>Hope this helps :)</em>
Answer:
C
Step-by-step explanation:
Use the circle area formula.
A = pi * r^2
A = pi * 4^2
A = pi * 16
A = 50.27