Which of the graphs below correctly solves for x in the equation -x² + 2x + 6 = 2x - 3?

Solution:

Quadratic equations are those equations whose degree is equal to two. They are used for calculations in many fields of engineering and science as well as advanced mathematics.

Given equation: -x² + 2x + 6 = 2x - 3

Now, to solve the equation for x, we follow the steps below:

⇒ -x² + 2x + 6 = 2x - 3

⇒ -x² + 2x − 2x = -6 - 3

⇒ -x² = -9

⇒ x² = 9

Hence, x = 3, or x = -3.

Now, we plot the result on the graph below.

Therefore, The graph cuts the x-axes at (-3, 0) and (3, 0).

Hence, the solution of the equation given is x = 3 and x = -3. It is represented as two straight lines on the cartesian plane.