Answer:
The vertex form is y = (x + 4)² - 13
The minimum value of the function is -13
Step-by-step explanation:
∵ y = x² + 8x + 3
∵ 8x ÷ 2 = 4x ⇒ (x) × (4)
∴ We need ⇒ x² + 8x + 16 to be completed square
∴ y = (x² + 8x + 16) - 16 + 3 ⇒ we add 16 and subtract 16
∴ y = (x + 4)² - 13 ⇒ vertex form
∵ The vertex form is (x - a)² + b
Where a is the x-coordinate of the minimum point and b is y-coordinate of the minimum point (b is the minimum value of the function)
∴ The minimum value is -13
Answer: 480 units^2
IN DEPTH EXPLANATION TO HELP YOU FOR FUTURE PROBLEMS:
Front:
b*h/2 = sa
12*5/2 = 30
Front = 30 units^2
Back:
b*h/2 = sa
12*5/2 = 30
Back = 30 units^2
Right:
w*l = sa
14*13 = 182 units^2
Right: 182 units*2
(figures out the length by using
pythagorean theorem)
Left:
w*l = sa
5*14 = 70 units^2
Left: 70 units^2
Bottom:
w*l = sa
12*14 = 168 units^2
ADD ALL THE UNITS:
168 + 70 + 182 + 30 + 30 = 480
See the attached picture:
<u>Answer:</u>
Equation for the curve in its final position is y = 2tan( x + 1 ) + 7.
<u>Step-by-step explanation:</u>
We have to find equation for the curve of y=tan(x) ,with following transformations:
<em>vertically stretched by a factor of 2:</em> y = 2tan(x)
<em>shifted a distance of 1 units to the left:</em> y = 2tan( x+1 )
<em>translated 7 units upward:</em> y = 2tan( x + 1 ) + 7
21!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
(19)
