Question

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

Answer 1

Answer:A. C. D

Explanation:

Answer 2

we will select each options and find zeros

(a)

`g(x)=x^2-4x-21`

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

and then we can solve for x

`g(x)=x^2-4x-21=0`

now, we can factor it

`(x-7)(x+3)=0`

we get

`x=7,x=-3`

so, this is TRUE

(b)

`g(x)=(x-3)(x+7)`

we can set it to 0

and then we can solve for x

`g(x)=(x-3)(x+7)=0`

we get

`x=3,x=-7`

so, this is FALSE

(c)

`g(x)=3x^2-12x-63`

we can set it to 0

and then we can solve for x

`g(x)=3x^2-12x-63 =0`

`3(x^2-4x-21) =0`

`3(x-7)(x+3) =0`

`x=-3,x=7`

so, this is TRUE

(d)

`g(x)=-(x+3)(x-7)`

now, we can set it to 0

and then we can solve for x

`g(x)=-(x+3)(x-7)=0`

`x=-3,x=7`

so, this is TRUE

(e)

we have

`g(x)=x^2+4x-21`

now, we can set it to 0

and then we can solve for x

`g(x)=x^2+4x-21=0`

`(x+7)(x-3)=0`

`x=-7,x=3`

so, this is FALSE