Please I need help with this question! :)
Answers
Since the question doesn't specify what type of equation it is, I'm going to explain how to write it in factored form.
f(x) = a(x +3)(x-5), I got this based off the x-intercepts. Basically, you want to design each binomial so when it's equal to 0 it would give you the x-intercept. Reach out if you need further explanation.
ex. (x+3) = 0, therefore, x = -3
Then, solve for the a value, the a value decides if the graph shrinks or stretches.
Without the 'a' value, the y intercept is currently at (0,-15) because if you plugged in 0 you would get (3)(-5) = -15.
Therefore, in order to get -75, you would need to have the 'a' value to 5.
Therefore, the equation is, (change name accordingly)
f(x) = 5(x+3)(x-5)
Step 2:
Find the middle value between the x intercepts; which is 1.
Plug 1 into the equation
f(1) = 5(1 + 3)(1 -5)
f(1) = 5(4)(-4)
f(1) = -80
The vertex is at (1, -80)