Mathematics, 28.06.2019 02:30 gatorboy1788

Suppose f(x)=x^2 and g(x)=5x^2. which statement best compares the graph of g(x) with the graph of f(x)? a) the graph of g(x) is the graph of f(x) horizontally stretched by a factor of 5 b) the graph of g(x) is the graph of f(x) vertically compressed by a factor of 5 c) the graph of g(x) is the graph of f(x) vertically stretched by a factor of 5 d) the graph of g(x) is the graph of f(x) shifted 5 units right

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Answer from: olivasm5626

Step-by-step explanation:

A vertical stretch of a function means the output values have changed by a factor or multiplication by a number. Recall, a quadratic function has the basic form $f(x)=x^{2}$ .

Our function g(x) is $5x^{2}$ meaning any value out of f(x) will be multiplied by 5 and the values increase by a factor of 5. This is a vertical stretch.

The statement that reads "the graph of g(x) is the graph of f(x) vertically stretched by a factor of 5" is correct.

Answer from: wycentliver1859

Option c - The graph of g(x) is the graph of f(x) vertically stretched by a factor of 5.

Step-by-step explanation:

Given : Suppose f(x)=x^2 and g(x)=5x^2

To find : Which statement best compares the graph of g(x) with the graph of f(x)?

Solution :

f(x)=x^2 and g(x)=5x^2

The graph of g(x) is multiplied by 5 of f(x) shows the vertical stretch.

Vertically stretch :

When y=f(x) → y=bf(x) i.e, the graph is b unit vertically stretched and b>1.

In the graph of f(x)=x^2 → f(x)=5x^2=g(x) i.e, 5 unit is multiplied.

Therefore, Option c is correct i.e, the graph of g(x) is the graph of f(x) vertically stretched by a factor of 5.

Answer from: Quest

answer: 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

step-by-step explanation:

Answer from: Quest

solution:

the given function is ,

$f(x) = 4 x^3 - 72 x^2 + 320 x,$

= $4x( x^2- 18 x + 80)\\\\ 4 x(x^2-10 x -8 x + 80) \\\\ 4 x[(x-10)(x-8)]$

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

$f(x) = a x^3+ b x^2 + c x+d,$

sum of the roots = a + b +c= 0+8+10=18= $\frac{-b}{a}$

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 = $\frac{c}{a}$

product of roots = a b c = 0= $\frac{d}{a}$

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function $f(x) = 4 x^3 - 72 x^2 + 320 x,$ is given by entry and exit route of this hall.