Answer:
The correct answer is A.
Step-by-step explanation:
In order to find the correct answer, we simply need to find the values of x where the two graphs are equal to each other. In order to do so, we set the two equations equal to each other and solve for the two x values.
x^2 + 3 = x + 4 -----> Subtract x
x^2 - x + 3 = 4 ------> Subtract 4
x^2 - x - 1 = 0
Now that we have this equal to 0, we can use the quadratic formula to solve. Below is the quadratic equation.
[tex]\frac{-b +/- \sqrt{b^{2} - 4ac } }{2a}[/tex]
For this, we use the coefficient of x^2 as a, the coefficient of x as b and the constant as c. Below is the work for when we plug into the equation.
[tex]\frac{-(-1) +/- \sqrt{(-1)^{2} - 4(1)(-1) } }{2(1)}[/tex]
[tex]\frac{1 +/- \sqrt{5} }{2}[/tex]
[tex]\frac{1 + \sqrt{5} }{2}[/tex] OR [tex]\frac{1 - \sqrt{5} }{2}[/tex]
1.6 OR -0.6
These two numbers are the x values for part A, which means it is the proper intersections.
