Answer:
#1
Zeroes: x = 4, x = -6
The vertex is at ( -1 , 50 )
Step-by-step explanation:
I'll do the first one, you try the rest
All of these are written in y = a(x - x1)(x - x2) where x1 and x2 are given and x are the two different zeroes (or x-intercepts)
f(x) = -2(x-4)(x+6)
The zeroes are x - 4 = 0 and x + 6 = 0 if you solve, you get 4 and -6
Zeroes: x = 4, x = -6
The x value of the vertex can be found using -b/2a (in the form ax^2 + bx + c)
First expand f(x)
-2(x^2 + 2x - 24) => -2x^2 - 4x + 48
b = -4 and a = -2
-(-4)/2(-2) = 4/-4 = -1
the x-value of the vertex is -1
Now substitute -1 as x to find the y-value of the vertex
-2(-1-4)(-1+6) = -2(-5)(5) = 50 <= y-value of vertex
The vertex is at ( -1 , 50 )
