It's a Quadratic that doesn't have any real roots as the parabola doesn't cross the x-axis.
For graphing:
If you're familiar with the parabola of y=x^2, then you could graph that but just translate it upwards by +4 on the y such that f(x)+4 will be equal to it.
If you aren't, then we know the y-intercept is 4, and that's also the point of the minimum point of the curve. If I were you, I'd write a table of some of the integer values:
x y
-2 8
-1 5
0 4
1 5
2 8
The value of y is the same for x and -x as anything squared is positive.This means that there is a line of symmetry in the y-axis.
This then makes it much easier to graph, simply place these points on the graph and make sure the curve is exponential. This means the gradient (steepness) gets greater the bigger the value of x.
Answer
Step-by-step explanation:
You multiply 1 1/2 by 5 (because you give it to them 5 times a day) and you get 7 1/2 then you have to multiply that by 4 (because you’re calculating how much over 4 days) and you get 30oz .
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)
