Answer:
[tex]\huge\boxed{\text{(D) 20}}[/tex]
Step-by-step explanation:
Our first goal is here to try and find the values of x that these equations meet at. We can then plug in the x-values into one of the equations (since their x values will be the same) and find the corresponding y value.
To find the x value that satisfies both equations, we can set both expressions equal to each other.
[tex]x^2 - 2x - 15 = 2x+6[/tex]
We can now solve for x.
Subtract 2x from both sides:
Subtract 6 from both sides:
We now have a polynomial in the form [tex]ax^2 + bx + c[/tex] ! We can factor this by finding two numbers that:
(A) When multiplied, get us [tex]c[/tex] (-21)
(B) When added together, get us [tex]b[/tex] (-4)
We know that [tex]-7 \cdot 3 = 21[/tex] and [tex]-7 + 3 = -4[/tex].
Therefore our factorization is [tex](x+3)(x-7)[/tex], so the points at which these functions meet are -3 and 7.
We can now plug both of these values into one of the equations to find it's y value. Let's use [tex]2x+6[/tex] (easier to work with).
-3:
[tex]2(-3) +6\\\\-6+6=0[/tex]
7:
[tex]2(7)+6\\\\14+6\\\\20[/tex]
Since 0 isn't an option on the list, that means that (D) 20 would be a point of intersection of the two graphs.
Hope this helped!
