select the approximate value

Question

Select the approximate values of x that are solutions to f(x) = 0, where
f(x) = -3x2 + 2x + 2.

A. {–0.55, 1.22}

B. {-3, 2}

C. {–0.67, –0.67}

D. {–1.50, 1.00}

Answer 1

Hi Gina-

 

You are being asked to find the roots of the quadratic equation

0 = -3x^2 +2x +2

That is where the graph of that equation crosses the X-axis.

 

Using the Quadratic Formula

(-b +/- Squareroot[b2 - 4ac])/2a

 

(-2 +/- Squareroot[2^2 -4(-3)(2)]/2(-3)

 

(-2 +/- Squareroot[28])/-6

 

(-1 +/- Squareroot[7])/-3

 

x = -0.55

x= 1.22

 

Answer 2

Using completion of the square:

 

f(x) = -3x² + 2x

0 = -3(x² - 2x/3       ) + 2

-2 = -3(x2 - 2x/3 )

-2 = -3(x² - 2x/3 + (1/3)²) + 3(1/3)²

-2 = -3(x - 1/3)² + 7/3

-7/3 = -3(x - 1/3)²

7/9 = (x - 1/3)²

±√7 / 3 = x - 1/3

(1 ± √7) / 3 = x

 

x ∈ { 1.22, -0.548 }

 

A.