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Sanjay graphs a quadratic function that has x-intercepts of –3 and 7. Which functions could he have graphed?

Check all that apply.

g(x) = x^2 – 4x – 21

g(x) = (x – 3)(x + 7)

g(x) = 3x^2 – 12x – 63

g(x) = –(x + 3)(x – 7)

g(x) = x^2 + 4x – 21

Respuesta :

we will select each options and find zeros

(a)

[tex] g(x)=x^2-4x-21 [/tex]

for finding x-intercept , we can set g(x)=0

and then we can solve for x

[tex] g(x)=x^2-4x-21=0 [/tex]

now, we can factor it

[tex] (x-7)(x+3)=0 [/tex]

we get

[tex] x=7,x=-3 [/tex]

so, this is TRUE

(b)

[tex] g(x)=(x-3)(x+7) [/tex]

we can set it to 0

and then we can solve for x

[tex] g(x)=(x-3)(x+7)=0 [/tex]

we get

[tex] x=3,x=-7 [/tex]

so, this is FALSE

(c)

[tex] g(x)=3x^2-12x-63 [/tex]

we can set it to 0

and then we can solve for x

[tex] g(x)=3x^2-12x-63 =0[/tex]

[tex] 3(x^2-4x-21) =0[/tex]

[tex] 3(x-7)(x+3) =0[/tex]

[tex] x=-3,x=7[/tex]

so, this is TRUE

(d)

[tex] g(x)=-(x+3)(x-7) [/tex]

now, we can set it to 0

and then we can solve for x

[tex] g(x)=-(x+3)(x-7)=0 [/tex]

[tex] x=-3,x=7 [/tex]

so, this is TRUE

(e)

we have

[tex] g(x)=x^2+4x-21 [/tex]

now, we can set it to 0

and then we can solve for x

[tex] g(x)=x^2+4x-21=0 [/tex]

[tex] (x+7)(x-3)=0 [/tex]

[tex] x=-7,x=3 [/tex]

so, this is FALSE

Answer:A.  C. D

Step-by-step explanation:

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