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
F ( x ) = x² + 8 x - 6 = x² + 8 x + 16 - 16 - 6 =
= ( x + 4 )² - 22
Coordinates of the vertex : ( - 4, - 22 )
ANSWER
EXPLANATION
We want to simplify;
Simplify the fraction:
This is now the same as:
We perform the subtraction to obtain,
Therefore
Solution
Since the sum of the consecutive angles of a parallelogram is equal to 180°, the two other consecutive angles of the parallelogram have the angle measure
180°- 36° = 144°.
Since the opposite angles of a parallelogram are congruent, the angle opposite to the given one of 36° has the angle measure of 36° too.
Answer. The rest of the angles of the parallelogram have the angle measure of 144° (the consecutive angle), 36° (the opposite angle), and 144° (the second consecutive angle).
