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3 years ago

Which equation, when graphed, has x-intercepts at (2, 0) and (4, 0) and a y-intercept of (0, –16)?

Mathematics

2 answers:

kenny6666 [7]3 years ago

5 0

Answer: The correct option is (C) $f(x)=-2(x-2)(x-4).$

Step-by-step explanation: We are given to select the correct equation such that its graph has x-intercepts at (2, 0) and (4, 0) and a y-intercept of (0, –16).

We know that the co-ordinates of the x-intercepts and the y-intercept will satisfy the equation.

So, we will check the given functions one by one.

Option (A) is

$f(x)=-(x-2)(x-4).$

Here,

$f(2)=-(2-2)(2-4)=0,\\\\f(4)=-(4-2)(4-4)=0,\\\\f(0)=-(0-2)(0-4)=-8\neq -16.$

So, this option is not correct.

Option (B) is

$f(x)=-(x+2)(x+4).$

Here,

$f(2)=-(2+2)(2+4)=-24\neq 0.$

So, this option is not correct.

Option (C) is

$f(x)=-2(x-2)(x-4).$

Here,

$f(2)=-2(2-2)(2-4)=0,\\\\f(4)=-2(4-2)(4-4)=0,\\\\f(0)=-2(0-2)(0-4)=-16.$

So, this option is correct.

Option (D) is

$f(x)=-2(x+2)(x+4).$

Here,

$f(2)=-2(2+2)(2+4)=-48\neq 0.$

So, this option is not correct.

Thus, The correct equation is $f(x)=-2(x-2)(x-4).$

Option (C) is correct.

vova2212 [387]3 years ago

3 0

f(x)= -2 (x - 2) ( x - 4)

if x=2 ⇒ f(x)=y=0 ⇒ graph of f(x) intercept x axis in (2,0)
if x=4 ⇒ f(x)=y=0 ⇒ graph of f(x) intercept x axis in (4,0)
if x=0 ⇒f(x)= -2 *(-2)*(-4)= - 16 ⇒ graph of f(x) intercept y axis in (0,- 16)

⇒ f(x)= -2 (x - 2) ( x - 4) is the answer

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A gardener already has four and one over 2 ft of fencing in his garage. He wants to fence in a square garden for his flowers. Th

NikAS [45]

<h2>Answer:</h2>

$6\frac{1}{2}$ <u>, "six and one over two ft".</u>

<h2>Step-by-step explanation:</h2>

Let's considerate the fact that the garden has a <u>square shape</u>.

<h3>1. Finding values of interest.</h3>

Amount of fence that the gardener already has: $4\frac{1}{2}$ ft.

Length of one side: $2\frac{3}{4}$ ft.

If one side measures $2\frac{3}{4}$ ft, and the square garden has 4 sides of equal length, because it's a square, then we must multiply the measure of one side by 4 to find the total length of fence needed:

$4*(2\frac{3}{4})=\\ \\4*(2+\frac{3}{4})=\\ \\(4*2)+(4*\frac{3}{4})=\\ \\8+(\frac{12}{4} )=\\ \\8+3=\\ \\11$

The gardener already has $4\frac{1}{2}$ , which equals $4 + \frac{1}{2}$ . Hence, the difference between the amount needed and the amount that the gardeneralready has will give us the remaining amount required. Let's do that: