Find the zeroes of the function f(x)=(x-3)^2-49

Answer 1

To find the zeros or solutions set the equation equal to 0

(x-3)^2 - 49=0

(x-3)^2 = 49

x-3 = 7 x=10 and

x-3 = -7 x= -4

So our solutions or zeros are x=10 and x=-4

Answer 2

1. Expand: (x - 3)² becomes x² - 6x + 9
2. Add: x² - 6x - 40
3. Find roots: (x + 4) (x - 10)
4. Set equal to zero: x + 4 = 0 and x - 10 = 0
5. Solve: x = 10 and x = -4

Answer 3

Find the zeros often means find the x values when y (of f(x)) equals zero.

So, we are solving 0=(x-30)²-49

When I solve equations like this one, I begin by foiling.

0= x²-60x+900-49

0= x²-60x+851

Since I do not see any reasonable factors of the polynomial, I would use the quadratic equation.

x= 60±√((-60)²-4(1)(851))/2(1)

(60+ √3600-3404)/2

(60+√196)/2

(60+14)/2

74/2

x=37

(60-√3600-3404)/2

(60-√196)/2

(60-14)/2

46/2

x=23

So the zeros are 37 and 23