Which of the graphs below correctly solves for x in the equation −x2 + 2x + 6 = 2x − 3?
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.
Answer: The solution of the equation given is x = 3 and x = -3. It is represented as two straight lines on the cartesian plane.
Let's understand the solution in detail.
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).