Determining the zeros means that you are looking for the x-intercept of the function....
You can factor this function ....
QUADRATIC FORMULA : ax^2 + bx + c
f(x) = - 8 x^2 + 2x + 1
Set f(x) to 0 and factor the expression....
0 = - 8 x^2 + 2x + 1
Get everything to the left side... because variables have to be on the left side
8x^2 - 2x - 1 = 0
Now factor... a = 8 , b = -2 , c = - 1
To factor... Start by multiplying a * c => 8 * -1 => - 8
Now you have to find two numbers that multiply to -8 and add up to b which is -2
We could use - 4 and 2 because... - 4 * 2 = - 8
- 4 + 2 = - 2
Now you rewrite the expression....
8x^2 - 4x + 2x - 1
Now take out common factors...
4x ( 2x - 1 ) + 1 ( 2x - 1 )
( 2x - 1 ) ( 4x + 1 )
Now you have to write two separate equations and solve for x...
( 2 x - 1 ) ( 4x + 1 )
2x - 1 = 0 4x + 1 = 0
Add one to both sides.. Subtract 1 from both sides...
2x = 1 4x = - 1
Divide by 2 to x by its self... Divide by 4
x = 1/2 x = - 1/4
The zeros of f(x) = - 8 x^2 + 2x + 1 are 1/2 and -1/4