Mathematics, 08.09.2019 05:20 ringo12384

(a) express f(x) = x^2 - 8x + 22 in the form f(x) = (x +a)^2 +b, where a and b are constants to be determined. (b) state the minimum value of f(x) and the value of x at which the minimum occurs. (c) solve the inequality x^2 - 8x + 22 > 10.

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Answer from: SmolBeanPotato

(x -4)² +6minimum value: at x = 4(x < 2) ∪ (6 < x) . . . for f(x) > 10

Step-by-step explanation:

(a) You can split the constant so it includes a portion that is the square of half the x-coefficient:

f(x) = x² -8x +16 +6

Now, that first trinomial can be written as the square you want:

f(x) = (x -4)² +6

(b) The form in part (a) is "vertex form" where (-a, b) is the vertex. When the coefficient of x² is positive, as here, the parabola opens upward, and its vertex is its minimum.

The minimum occurs at (4, 6), where x=4.

f(x) > 10

(x -4)² +6 > 10 . . . substitute the vertex form of f(x)

(x -4)² > 4 . . . . . . . subtract 6

|x -4| > 2 . . . . . . . . take the square root

This means two things:

-2 > x -4 ⇒ 2 > x

and

x -4 > 2 ⇒ x > 6

Then the solution to the inequality is (x < 2) ∪ (6 < x).

_____

You can see the vertex in the attached graph, and that f(x) > 10 for x outside the interval [2, 6].

(a) express f(x) = x^2 - 8x + 22 in the form f(x) = (x +a)^2 +b, where a and b are constants to be d

Answer from: Quest

step-by-step explanation:

the total is 23.97. 0.25% is off so you have to subtracting 25% from 100% and you will get 75% if you convert it to decimal you will get 0.75. you have to find the original because the formula is % times original = total.so you have the total and the % so you just have to plug it in.

Answer from: Quest

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2 is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes. our only condition is that it passes through the point (-2,5)

A. write an equation of a line that passes through (-2, 5). b. how many different equations could y

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(a) express f(x) = x^2 - 8x + 22 in the form f(x) = (x +a)^2 +b, where a and b are constants to be d...

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