y = x^2 + 32x - 4
To use the quadratic formula to find the zeroes, we need to make sure the equation is written in the form color(red)(a)x^2 + color(magenta)(b)x + color(blue)(c) = 0, which this equation is.
So we know that:
color(red)(a = 1)
color(magenta)(b = 32)
color(blue)(c = -4)
The quadratic formula is x = (-color(magenta)(b) +- sqrt(color(magenta)(b)^2 - 4color(red)(a)color(blue)(c)))/(2color(red)(a)).
Now we can plug in the values for color(red)(a), color(magenta)(b), and color(blue)(c) into the quadratic formula:
x = (-color(magenta)(32) +- sqrt((color(magenta)(32))^2 - 4(color(red)(1))(color(blue)(-4))))/(2(color(red)(1)))
Simplify:
x = (-32 +- sqrt(1024 + 16))/2
x = (-32 +- sqrt(1040))/2
x = (-32 +- 4sqrt65)/2
x = -16 +- 2sqrt65
This is the same thing as:
x = -16 + 2sqrt65 and x = -16 - 2sqrt65
because +- means "plus or minus."
Hope this helps!
