Question

How do I find the x intercepts of the function
f(x) = -6x^2 + 2700x - 63,750

I know the y has to = 0, but I'm not sure how to solve for x....

Thank you.

Answer 1

factor or use the quadratic formula
-6x^2 + 2700x - 63,750 = -6(x-25)(x-425)
That is zero when x = 25 or 425

The quadratic formula also works. It says that
x = (-2700±√(2700^2-4(-6)(-63750)))/-12
= (2700±2400)/12
= 225±200
= 25 or 425

Answer 2

x intercept is a point where f(x) = 0

So you must sove equation:

- 6 x² + 2 700 x - 63 750 = 0

- 6 ∙ ( x² - 450 x + 10 625 ) = 0

Divide both sides by - 6

x² - 450 x + 10 625 = 0

Solve this equation usngquadratic formula.

x₁/₂ = [ - b ± √ ( b² - 4 ac ) ] / 2 a

In this case:

a = 1 , b = - 450 , c = 10 625

x₁/₂ = [ - ( - 450 ) ± √ ( ( - 450 )² - 4 ∙ 1 ∙ 10 625 ) ] / 2 ∙ 1 =

[ 450 ± √ ( 202 500 - 42 500) ] / 2 =

( 450 ± √ 160 000) / 2 =

( 450 ± 400 ) / 2 =

2 ∙ ( 225 ± 200 ) / 2 = 225 ± 200


x₁ = 225 - 200 = 25

x₂ = 225 + 200 = 425

So x intercepts:

( x₁ , 0 ) , ( x₂ , 0 )

( 25 , 0 ) , ( 425 , 0 )