Question

20 points
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) = x2 – 4x – 21

g(x) = (x – 3)(x + 7)

g(x) = 3x2 – 12x – 63

g(x) = –(x + 3)(x – 7)

g(x) = x2 + 4x – 21

Answer 1

Given: x-intercepts are –3 and 7.

To find: Which functions could he have graphed.

Solution:

• As we have given the intercepts which can be said as the roots of the quadratic equation, that are -3 and 7, so we need to find the roots of the given equations to verify.
• (a) g(x) = x2 – 4x – 21  = 0

               (x-7)(x+3) = 0

               x=7, -3

            So this is same as given intercepts, so this is true.

• (b) g(x) = (x – 3)(x + 7)  = 0

           As we can see that in this, x comes out to be 3 and -7 which is not equal to given intercept so this is false.

• (c) g(x) = 3x2 – 12x – 63  = 0

              3( x2 - 4x - 21) = 0

             So this is same as the equation in (a) so its roots will be 7 and -3, so its true.

• (d) g(x) = –(x + 3)(x – 7)  = 0

             In this x comes out to be -3 and 7, so it is true as it satisfies the given intercepts.

• (e) g(x) = x2 + 4x – 21 = 0

             (x+7)(x-3) = 0

             x= -7, 3

            So this do not satisfies the given intercept so its false.

Answer:

                He would have graphed the following functions:

                g(x) = –(x + 3)(x – 7) ,  g(x) = 3x2 – 12x – 63,   g(x) = x2 – 4x – 21

Answer 2

Answer:

A, C, D

Step-by-step explanation:

just did this one