Find the zeros of the quadratic function by completing the square. List the x-intercepts of the graph of the function.
-$$g ( x ) = 4 x ^ { 2 } - 2 x - 6$$
A) $x = \frac { 3 } { 2 } , x = - 1$
B) $x = \frac { 2 } { 3 } , x = 1$
C) $x = \frac { 2 } { 3 } , x = 0$
D) $x = \frac { 2 } { 3 } , x = - 1$

Question

Quizplus · Accepted Answer

To complete the square, add and subtract the square of half the coefficient of the linear term:$4x^2 - 2x - 6 = 4x^2 - 2x + \frac{1}{4} - \frac{1}{4} - 6$$= (2x - \frac{1}{2})^2 - \frac{25}{4}$$= (2x - \frac{1}{2})^2 - (\frac{5}{2})^2$Now, factor the difference of squares:$= (2x - \frac{1}{2} + \frac{5}{2})(2x - \frac{1}{2} - \frac{5}{2})$$= (2x + 2)(2x - 3)$$= 4x^2 - 6x + 4x - 6$$= 4x^2 - 2x - 6$Therefore, the zeros of the function are $x = \frac{3}{2}$ and $x = -1$.

Find the Zeros of the Quadratic Function by Completing the Square