Mathematics, 15.01.2020 00:31 xojade

Two quadratic functions are represented below.

in two or more complete sentences, explain how you can determine the maximum value of the quadratic functions, f(x) and g(x).
which function has the greater maximum value, f(x) or g(x)?

Answers: 2

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Answer from: jb230

To determine the maximum value of a quadratic function opening downwards, we are going to find the vertex; then the y-value of the vertex will be our maximum.
To find the vertex (h,k) (where h=x-coordinate and k=y-coordinate) of a quadratic function of the form $f(x)=a x^{2} +bx+c$ we'll use the vertex formula: $h= \frac{-b}{2a}$ , and then we are going to replace that value in our original function to find k.

So, in our function $f(x)=- x^{2} +4x-3$ , a=-1

and

.
Lets replace those values in our vertex formula:
$h= \frac{-4}{2(-1)}$
$h= \frac{-4}{-2}$
h=2

Now that we know the x-coordinate of our vertex, lets replace it in the original function, to get the y-coordinate:
$h=f(2)=-(2^{2} )+4(2)-3$
h=-4+8-3

We just prove that the vertex of f(x)

is (2,1), and for the graph we can tell that the vertex of g(x)

is (-2,4). The only thing left is compare their y-coordinates to determine which one has the greater maximum value. Since 4>1, we can conclude that g(x)

has the greater maximum.
Two quadratic functions are represented below. in two or more complete sentences, explain how you ca

Answer from: Quest

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2 polynomial long division

dividing : x4+5x3-4x2-8x+6

("dividend")

by : x-1 ("divisor")

dividend x4 + 5x3 - 4x2 - 8x + 6

- divisor * x3 x4 - x3

remainder 6x3 - 4x2 - 8x + 6

- divisor * 6x2 6x3 - 6x2

remainder 2x2 - 8x + 6

- divisor * 2x1 2x2 - 2x

remainder - 6x + 6

- divisor * -6x0 - 6x + 6

remainder 0

quotient : x3+6x2+2x-6 remainder: 0

Answer from: Quest

alright well the answers to your question is

2xy/9 hope this have a nice day : )

step-by-step explanation:

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Two quadratic functions are represented below.

in two or more complete sentences, explai...

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