select the approximate values of x that are solutions to f(x)=0, where f(x)=-4x^2 +3x +9

Question

multiple choice:  a) (192, -1.17)  b) (-4, 3)  c) (-0.75, -2.25)  d) (-044, 0.33)

Answer 1

For this problem, they tell us f(x)=-4x²+3x+9 and want us to solve for x when f(x)=0

 

If 0=f(x)=-4x²+3x+9 

then 0=-4x²+3x+9 

This is a quadratic equation. There are several method for solving this kind of equation and we need to choose the best method for this problem:

• factoring-only works if it is factorable
• square root method- useful in special cases
• Complete the square- always works but is time consuming
• Quadratic Formula- always works but requires memorization

For this kind of problem factoring is usually the fastest method (if it works), but since the quadratic equation always works so that is the method I will use here.

 

Quadratic Formula for 0=ax²+bx+c:

 

x=[-b±√(b²-4ac)]/2a

 

For our problem: (look at coefficients)

a=-4

b=3

c=9

 

x=[-b±√(b²-4ac)]/2a

x=[-3±√(3²-4(-4)(9))]/2(-4)

x=[-3±√(9+144)]/(-8)

x=[-3±√(156)]/(-8)

x=[-3±√(9+144)]/(-8)

(use calculator)

x=[-3±12.37]/(-8)

 

this is really 2 equations:

x=[-3+12.37]/(-8) and x=[-3-12.37]/(-8)

(use calculator)

x=-1.17                   and x=1.92