Hello there!
There are two ways to find the minimum value of this function, but before I show you how, I am going to teach you a little bit about minimum value.
The minimum value on a parabola is the vertex or turning point. This means that the slope of the tangent line is horizontal, having a slope of 0.
The algebraic way to find the minimum or maximum value on a parabola is to use the formula -b/2a. Let's do it...
y=4x^2+4x-35
where a=4, b=4, and c=-35
-b/2a
-4/2(4)
-4/8
-1/2
Now let me show you the other way...
Take the derivative of
y=4x^2+4x-35
y'=8x+4
And set it equal to 0...
8x+4=0
8x=-4
x=-1/2
We got the same answer. Now that we know x=-1/2, plug this into the original equation to find y.
y=4x^2+4x-35
y=4(-1/2)^2+4(-1/2)-35
y=-1-2-35
y=-38
So the minimum point on this parabola is (-1/2,-38)
I really hope th
Completing the square is a process to find the solutions, or the x-values, to a quadratic equation. This method can only work if it is in the format: x^2 + bx = c
In this equation, the b value is -12 and the c value is -6. The process for completing the square goes like this:
x^2 + bx + (b/2)^2 = c + (b/2)^2
Now let’s solve the equation above using this method.
Step 1: x^2 - 12x + (-12/2)^2 = -6 + (-12/2)^2
Step 2: x^2 - 12x + (-6)^2 = -6 + (-6)^2
Step 3: x^2 - 12x + 36 = -6 + 36
Step 4: x^2 - 12x + 36 = 30
Now, to factor it. After doing the process until now, the left side of the equation can ALWAYS be in the format: (x + a)^2
Step 5: x^2 - 12x + 36 can be factored in this format as (x - 6)^2
Step 6: (x - 6)^2 = 30
Step 7: x - 6 = √30
Step 8: x = 6 ±√30
Volume of a prism is base *hieght
Answer:
The area is 16.62
Step-by-step explanation:
The expression you use is pi x r squared. which is 3.14 x 2.3 x 2
