Kara earned $136.75 last week working 16 hours. She earned $10.50 per hour at the fast food restaurant and $4.25 per hour helping her aunt clean her store. How many hours did she work at the fast food restaurant? How many hours did she help her aunt clean the store? In your response make sure to:
Create a model that can be used to determine the number of hours Kara worked at each job.

#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 )