Answer:
functions: first one, third one, fifth one, seventh one, eigth one
the rest are not function
Step-by-step explanation:
if it is a function it either passes the line test or it doesnt have two outputs
There are 2 options to solve that.
1. The first one is by derivatives.
f(x)=x^2+12x+36
f'(x)=2x+12
then you solve that for f'(x)=0
0=2x+12
x=(-6)
you have x so for (-6) solve the first equation, then you find y
y=(-6)^2+12*(-6)+36=(-72)
so the vertex is (-6, -72)
2. The second option is to solve that by equations:
for x we have:
x=(-b)/2a
for that task we have
b=12
a=1
x=(-12)/2=(-6)
you have x so put x into the main equation
y=(-6)^2+12*(-6)+36=(-72)
and we have the same solution: vertex is (-6, -72)
For next task, I will use the second option:
y=x^2-6x
x=(-b)/2a
for that task we have
b=(-6)
a=1
x=(6)/2=3
you have x so put x into the main equation
y=3^2+(-6)*3=(--9)
and we have the same solution: vertex is (3, -9)
Answer:
C
Step-by-step explanation:
the factor of x in the equation is the slope, which is the ratio y/x indicating how many units y changes, when x changes a certain amount of units.
going from the left point to the right point x changes by +3 units, and y changes by -1 unit.
so, the slope (and factor of x in the equation) is -1/3.
and the constant term in the equation is the y (axis) intercept of the line.
this is the y value, when x = 0 (intercepting the y axis).
and we see in the graph, when x = 0, the line goes through y = 2.
so, the equation has to be
y = -1/3 × x + 2
therefore, C is the right answer.
Answer:
Step-by-step explanation:
In y = mx + b form, the slope can be found in the m position and the y intercept can be found in the b position.
4x - 2y = -6
-2y = -4x- 6
y = (-4/-2)x -(6/-2)
y = 2x + 3....slope here is 2, and y int is 3
3x + y = 3
y = -3x + 3.....slope here is -3, and y int is 3
B. slopes are different, y intercepts are the same