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dexar [7]
2 years ago
9

Help me plsssssssss its easy and show work please

Mathematics
1 answer:
babymother [125]2 years ago
8 0

Answer:

» For x-intercept, y is zero

<u> </u><u>y</u><u> </u><u>=</u><u> </u><u>x²</u><u> </u><u>-</u><u> </u><u>1</u><u>2</u><u>x</u><u> </u><u>+</u><u> </u><u>3</u><u>2</u><u> </u>

{ \tt{0 =  {x}^{2} - 12x + 32 }} \\ { \tt{ {x}^{2} - 12x + 32 = 0 }} \\ { \tt{(x - 8)(x - 4) = 0}} \\ { \tt{x = 8 \:  \: and \:  \: 4}} \\  { \mathfrak{x - intercept :  \:  \: }}{ \boxed{ \tt{ \: (8, \: 0) \:  \: and \:  \: (4, \: 0) \:  \: }}}

<u> </u><u>y</u><u> </u><u>=</u><u> </u><u>x²</u><u> </u><u>-</u><u> </u><u>1</u><u>0</u><u>x</u><u> </u><u>+</u><u>2</u><u>4</u><u> </u><u>:</u>

{ \tt{0 =  {x}^{2}  - 10x + 24}} \\ { \tt{ {x}^{2}  - 10x + 24 = 0}} \\ { \tt{(x - 6)(x - 4) = 0}} \\ { \tt{x = 6 \:  \: and \:  \: 4}} \\ { \mathfrak{x - intercept :  \:  \: }}{ \boxed{ \tt{ \: (6, \: 0) \:  \: and \:  \: (4, \: 0) \:  \: }}}

<u> </u><u>y</u><u> </u><u>=</u><u> </u><u>x²</u><u> </u><u>+</u><u> </u><u>1</u><u>0</u><u>x</u><u> </u><u>+</u><u> </u><u>1</u><u>6</u><u> </u><u>:</u>

{ \tt{0 =  {x}^{2}  + 10x + 16}} \\ { \tt{ {x}^{2} + 10x + 16 = 0 }} \\ { \tt{(x + 2)(x + 8) = 0}} \\ { \tt{x =  - 2 \:  \: and \:  \:  - 8}} \\ { \mathfrak{x - intercept :  \:  \: }}{ \boxed{ \tt{ \: ( - 2, \: 0) \:  \: and \:  \: ( - 8, \: 0) \:  \: }}}

<u> </u><u>y</u><u> </u><u>=</u><u> </u><u>x²</u><u> </u><u>-</u><u> </u><u>2</u><u>5</u><u> </u><u>:</u>

{ \tt{0 =  {x}^{2}  - 25}} \\ { \tt{ {x}^{2}  = 25}} \\ { \tt{ \sqrt{ {x}^{2}  } =  \sqrt{25}  }} \\ { \tt{x =  \pm5}} \\ { \mathfrak{x - intercept :  \:  \: }}{ \boxed{ \tt{ \: (5, \: 0) \:  \: and \:  \: ( - 5, \: 0) \:  \: }}}

<u> </u><u>y</u><u> </u><u>=</u><u> </u><u>x²</u><u> </u><u>+</u><u> </u><u>8</u><u>x</u><u> </u><u>+</u><u> </u><u>1</u><u>2</u><u> </u><u>:</u>

{ \tt{0 =  {x}^{2} + 8x + 12 }} \\ { \tt{ {x}^{2} + 8x + 12 = 0 }} \\{ \tt{(x + 2)(x + 6) = 0}} \\ { \mathfrak{x - intercept :  \:  \: }}{ \boxed{ \tt{ \: ( - 2, \: 0) \:  \: and \:  \: ( - 6, \: 0) \:  \: }}}

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9514 1404 393

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  g(x) = x^2(x -5)

so has zeros at x=0 (multiplicity 2, meaning this is a local maximum*) and x=5.

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The local maximum is (0, 0); the local minimum is (10/3, -500/27). The graph is shown below.

_____

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