Answer:

Step-by-step explanation:

This is written in the standard form of a quadratic function:

where:
- ax² → quadratic term
- bx → linear term
- c → constant
You need to convert this to vertex form:

where:
To find the vertex form, you need to find the vertex. For this, use the equation for axis of symmetry, since this line passes through the vertex:

Using your original equation, identify the a, b, and c terms:

Insert the known values into the equation:

Simplify. Two negatives make a positive:

X is equal to 3 (3,y). Insert the value of x into the standard form equation and solve for y:

Simplify using PEMDAS:

The value of y is -6 (3,-6). Insert these values into the vertex form:

Insert the value of a and simplify:

:Done
 
        
             
        
        
        
Answer:
Step-by-step explanation:
Given the volume of the cylindrical soup expressed as V = πr³+ 7πr²
From V = πr³ + 7πr²;
factor out the common variable
V = πr³ + 7πr²
V = πr²(r+7) ... 1
The original volume of a cylinder V =  πr²h ....  2 where;
r is the radius of the cylinder
h is the height of the cylinder
Equating equation 1 and 2, we will have;
 πr²(r+7)  =  πr²h
Divide both sides by  πr²
 πr²(r+7)/ πr² = πr²h/ πr²
r+7 = h
h = r+7
<em>Hence the factor in the context given is equivalent to the height of the cylinder written as a function of its radius r</em>.<em> The statement means that the height of the cylindrical soup is 7 more than its radius.</em>
<em></em>
 
        
             
        
        
        
Answer:
Step-by-step explanation:
If we assume that the angle at A is 90 degrees.. which it does seem like it would be.  then use that the sum of the angles around the inside of a right triagle is 180 .   so  you have
180 = 37 + 90 + x 
53° = x  
does that help?