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can someone please help mee i need the right answers please(30 points and i will give brainliest!!!)

Can Someone Please Help Mee I Need The Right Answers Please30 Points And I Will Give Brainliest class=

Answer :

NAYEFXGO

Step-by-step explanation:

Funtion-A:

Given:

[tex]y = {x}^{2} - x - 6[/tex]

To find the x-intercepts set y to 0 and solve for x which is done below:

  • ⇒x²-x-6=0
  • ⇒(x-3)(x+2)=0
  • X=3 and -2

Therefore x-intercepts:(3,0),(-2,0)

To figure out the y-intercept , substitute 0 for x and simplify

  • ⇒y=0²-0-6
  • ⇒y=-6

Hence, The y-intercept is (0,-6)

  • The vertex (0.5,-6.25)

(skipped the steps as you've already figured it out)

Function-B:

Likewise A:

X-intercepts:

  • ⇒-x²+x+6=0
  • ⇒x²-x-6=0
  • ⇒x=3 and -2

Therefore,x-intercepts:(3,0),(-2,0)

Y-intercept:

⇒y=-0²+0+6

⇒y=6

Therefore, y-intercept (0,6)

The vertex:(0.5,6.25)

Inspection of the Parabolas:

The difference between the two parabolas is that The blue parabola is the result of reflection over x-axis of the red one.

View image NAYEFX

Answer:

a.

The x-intercepts are 3 and -2

The y-intercept is -6

The vertex is (1/2 , -25/4)

b.

The two parabola are symmetric across the x-axis

Step-by-step explanation:

x² - x - 6

[tex]=x^{2}-2\times \frac{x}{2} +\frac{1}{4} -\frac{1}{4}-6[/tex]

[tex]=(x-\frac{1}{2} )^{2} -(\frac{1}{4}+6)[/tex]

[tex]=(x-\frac{1}{2} )^{2} -\frac{25}{4}[/tex]

The x-intercepts :

(x-1/2)² = 25/4

Then

x - 1/2 = 5/2 or x - 1/2 = -5/2

Then

x = 3 or x = -2

The y-intercepts :

We get the y-intercept by replacing x by 0 in the trinomial :

0² - 0 - 6 = -6

b.

we notice that :

-x² + x + 6 = -(x² - x - 6)

Then

-x² + x + 6

[tex]=-(x-\frac{1}{2} )^{2} +\frac{25}{4}[/tex]

The x-intercepts :

[tex]-(x-\frac{1}{2} )^{2} +\frac{25}{4}=0[/tex]

⇔ (x-1/2)² = 25/4

Then

x - 1/2 = 5/2 or x - 1/2 = -5/2

Then

x = 3 or x = -2

The y-intercepts :

We get the y-intercept by replacing x by 0 in the trinomial :

0² + 0 + 6 = 6

View image PROFAROUK

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