Question

Help me plsssssssss its easy and show work please

Answer 1

Answer:

» For x-intercept, y is zero

y = x² - 12x + 32

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

y = x² - 10x +24 :

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

y = x² + 10x + 16 :

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

y = x² - 25 :

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

y = x² + 8x + 12 :

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

Answer 2

For x-intercepts, y is zero y = x² - 12x + 32 then x-intercept is (8,0) and (4,0)

For x-intercepts, y is zero y = x² - 10x + 24 then x-intercept is (6,0) and (4,0)

For x-intercepts, y is zero y = x² + 10x + 16 then x-intercept is (-2,0) and (-8,0)

For x-intercepts, y is zero y = x² - 25 then x-intercept is (5,0) and (-5,0)

For x-intercepts, y is zero y = x² + 8x + 12 then x-intercept is (-2,0) and (2,0)

What is x-intercepts?

X- intercepts is "x coordinates of a point where a line, a curve or surface intersects at x- axis".

According to the question,

a) y = x² - 12x + 32 (Put y=0)

x² - 12x + 32 = 0

(x-8) (x-4) = 0

x - 8 =0: x - 4 = 0

x = 8 and 4

x - intercept is (8,0) and (4,0)

b) y = x² - 10x + 24 (Put y=0)

x² - 10x + 24= 0

(x-6) (x-4) = 0

x - 6 = 0: x - 4 = 0

x = 6 and 4

x - intercept is (6,0) and (4,0)

c) y = x² + 10x + 16 (Put y=0)

x² + 10x + 16 = 0

(x+2) (x+8) = 0

x + 2=0: x + 8 = 0

x = -2 and -8

x - intercept is (-2,0) and (-8,0)

d) y = x² - 25 (Put y=0)

x² - 25 = 0

x² = 25

x = ± 5

x - intercept is (+5,0) and (-5,0)

e) y = x² + 8x + 12 (Put y=0)

x² + 8x + 12 = 0

(x+2) (x+6) = 0

x + 2=0: x + 6 = 0

x = 2,6

x - intercept is (2,0) and (6,0)

Learn more about X - intercepts here

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