Answer:
See graph in attachment
Step-by-step explanation:
We want to graph the function,
![g(x)=-2x^2-12x-24](https://tex.z-dn.net/?f=g%28x%29%3D-2x%5E2-12x-24)
First, let us rewrite the function in the vertex form;
![g(x)=-2(x^2+6x)-24](https://tex.z-dn.net/?f=g%28x%29%3D-2%28x%5E2%2B6x%29-24)
![\Rightarrow g(x)=-2(x^2+6x+(3)^2)--2(-3)^2-24](https://tex.z-dn.net/?f=%5CRightarrow%20g%28x%29%3D-2%28x%5E2%2B6x%2B%283%29%5E2%29--2%28-3%29%5E2-24)
![\Rightarrow g(x)=-2(x^2+6x+(3)^2)+2(9)-24](https://tex.z-dn.net/?f=%5CRightarrow%20g%28x%29%3D-2%28x%5E2%2B6x%2B%283%29%5E2%29%2B2%289%29-24)
![\Rightarrow g(x)=-2(x+3)^2+18-24](https://tex.z-dn.net/?f=%5CRightarrow%20g%28x%29%3D-2%28x%2B3%29%5E2%2B18-24)
![\Rightarrow g(x)=-2(x+3)^2-6](https://tex.z-dn.net/?f=%5CRightarrow%20g%28x%29%3D-2%28x%2B3%29%5E2-6)
The parabola opens downwards because ![a=-2\:](https://tex.z-dn.net/?f=a%3D-2%5C%3A%3C%5C%3A0)
The vertex of the parabola is
.
At y-intercept,
.
This implies that,
![g(0)=-2(0+3)^2-6=-18-6=-24](https://tex.z-dn.net/?f=g%280%29%3D-2%280%2B3%29%5E2-6%3D-18-6%3D-24)
At x-intercept, ![y=0](https://tex.z-dn.net/?f=y%3D0)
This implies that;
![\Rightarrow 0=-2(x+3)^2-6](https://tex.z-dn.net/?f=%5CRightarrow%200%3D-2%28x%2B3%29%5E2-6)
![\Rightarrow -2(x+3)^2=6](https://tex.z-dn.net/?f=%5CRightarrow%20-2%28x%2B3%29%5E2%3D6)
![\Rightarrow (x+3)^2=-3](https://tex.z-dn.net/?f=%5CRightarrow%20%28x%2B3%29%5E2%3D-3)
This equation has no real number solutions because of
on the right hand side. This implies that the graph has no x-intercepts.
We therefore draw a maximum graph through the vertex and the y-intercept to obtain the graph in the attachment.
Answer:
Step-by-step explanation:
ok so
4(x - 1) = – 4 + 4x
4x-4 = -4+4x
so Any value of ( x ) makes the equation true.
All numbers are a solution
For this case, the first thing to do is to graph the ordered pairs given in the problem.
Then, join the points to see the quadrilateral formed.
In this case the quadrilateral is a trapezoid.
The trapezoid is a geometric figure with four sides, of which only two are parallel.
Answer:
trapezoid
See attached image.
Answer:
![155.43 in^3](https://tex.z-dn.net/?f=155.43%20in%5E3)
Step-by-step explanation:
base*hight
![=> \pi r^2 = 3^2*\pi =9*3.14=28.26](https://tex.z-dn.net/?f=%3D%3E%20%5Cpi%20r%5E2%20%3D%203%5E2%2A%5Cpi%20%3D9%2A3.14%3D28.26)
![=> B*H=28.26*5.5=155.43\\](https://tex.z-dn.net/?f=%3D%3E%20B%2AH%3D28.26%2A5.5%3D155.43%5C%5C)
Answer:
a) A = 40*W – W^2
b) W = 20
c ) A = 400
Step-by-step explanation:
a) Let be
W = width W of the rectangle
L = lenght of the rectangle
P = Perimeter of the rectangle
A = area of the rectangle
P = 2*L + 2*W
80 = 2*L + 2*W
So, 2*L = 80 – 2*W
L = 40 – W
A = L * W
Replacing L
A = (40 – W)*W
A = 40*W – W^2
b) To find the máximum value for W, we derivate area and equal to zero
A’ = 40 – 2*W
40 – 2*W = 0
2*W = 40
W= 20
c) With the value for W, we find L
L = 40 – W
L = 40 – 20
L = 20
A = W*L
A = 20 * 20
A = 400