9514 1404 393
Answer:
- there are no points higher than a maximum; no points lower than a minimum
- average rate of change is the slope of a straight line connecting the points of interest.
Step-by-step explanation:
1. A point on a graph is a maximum if there are no points on the graph that are higher.
A point on a graph is a minimum if there are no points on the graph that are lower.
Sometimes you're interested in a "local" maximum or minimum. In that case, the "no points higher/lower" rule refers to points in the immediate vicinity of the one of interest.
Sometimes you're interested in a maximum or minimum on an interval. In that case, the rule applies to points contained within the interval. (The maximum or minimum may be at the end of the interval.)
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2. Average rate of change is defined over some interval. That is, you are given the end points of the interval of interest. The average rate of change is the slope of a straight line between those end points. The slope formula applies:
Answer:
-49x - 18 is the final answer!
Answer:
The factored form of this is (x - 7)(x -4)
Step-by-step explanation:
In order to factor quadratic equaitons with a 1 as the first coefficient, we look for two numbers that multiply to the last number (28), but add up to the middle number (-11). To do this, we often list the factors of the last number.
Factors of 28
1, 28
-1, -28
2, 14
-2, -14
4, 7
-4, -7
The numbers -4 and -7 satisfy this requirement and are therefore the numbers we want. Now we stick them into parenthesis along with x terms in the front like this:
(x - 7)(x -4)
And that is the fully factored form.
Since it is a polynomial
for the zero 4 you can write (x-4)
for the zero -14 you can write (x+14)
for the zero 5+8i since it is complex it will be accompanied with its conjugate 5-8i so you can write (x-(5+8i) and (x-(5-8i)) =(x^2-10x+89)
so
(x-4)(x+14)(x^2-10x+89)
expanding
x^4-67x^2+1450x-4984=0
--> y=2x^2+8x+5
Step 1: Group the first 2 terms together, separating them from the constant term.
--> (2 x X^2+{8}x X)+{5}
Step 2: Factor out leading coefficient, for completing the square to work, the coefficient of x2 must be 1.
--> 2 x (x^2+{4} x X) +{5}
Step 3: Complete the square, Take half of x coefficient and square it. Notice to keep equation balanced you must add this number and subtract it making the net effect zero.
--> 2 x(X^2{4}x X +4-4)+ {5}
--> 2 x(X+{2}^2 x 4) + {5}
Step 4: Distribute and add constants.
--> 2 x(X+{2}^2 -8+5
--> 2 x(X+{2}^2 +{-3}
Now it is successfully in vertex form and can be easily graphed.
The vertex is at (-2,-3)
The parabola opens up and has a y-intercept at (0, 5)
Here is a graph of this parabola:
