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AVprozaik [17]
3 years ago
6

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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Ex 3.6<br> 6. find the area enclosed between the curve y= -2x²-5x+3 and the x-axis
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When y=0,

-2{ x }^{ 2 }-5x+3=0\\ \\ 2{ x }^{ 2 }+5x-3=0\\ \\ \left( 2x-1 \right) \left( x+3 \right) =0

\\ \\ \therefore \quad x=\frac { 1 }{ 2 } \\ \\ \therefore \quad x=-3

--------------------

\int _{ -3 }^{ \frac { 1 }{ 2 }  }{ -2{ x }^{ 2 } } -5x+3dx

\\ \\ ={ \left[ -\frac { { 2x }^{ 2+1 } }{ 2+1 } -\frac { 5{ x }^{ 1+1 } }{ 1+1 } +3x \right]  }_{ -3 }^{ \frac { 1 }{ 2 }  }

\\ \\ ={ \left[ -\frac { 2{ x }^{ 3 } }{ 3 } -\frac { 5{ x }^{ 2 } }{ 2 } +3x \right]  }_{ -3 }^{ \frac { 1 }{ 2 }  }

\\ \\ \\ =\left\{ -\frac { 2 }{ 3 } { \left( \frac { 1 }{ 2 }  \right)  }^{ 3 }-\frac { 5 }{ 2 } { \left( \frac { 1 }{ 2 }  \right)  }^{ 2 }+3\left( \frac { 1 }{ 2 }  \right)  \right\} -\left\{ -\frac { 2 }{ 3 } { \left( -3 \right)  }^{ 3 }-\frac { 5 }{ 2 } { \left( -3 \right)  }^{ 2 }+3\left( -3 \right)  \right\}

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\\ \\ =-\frac { 2 }{ 24 } -\frac { 5 }{ 8 } +\frac { 3 }{ 2 } -\left\{ \frac { 54 }{ 3 } -\frac { 45 }{ 2 } -9 \right\}

\\ \\ =-\frac { 2 }{ 24 } -\frac { 15 }{ 24 } +\frac { 36 }{ 24 } -\frac { 54 }{ 3 } +\frac { 45 }{ 2 } +9

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\\ \\ =\frac { 343 }{ 24 }

Answer: 343/24 units squared.
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3 years ago
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