Question

At what point(s) do these graphs intersect? y+x^2=3x-5 and y=4x+1

Answer 1

Answer:

Incorrect. Graphs do not intersect

Step-by-step explanation:

Solution:-

- We are given two equations for the each plot as follows:

                            $y+x^2 = 3x - 5\\\\y = 4x + 1$

- To determine the coordinates of intersection of the two plots we will use direct substitution of equation 2 into 1:

                      $( 4x + 1 ) + x^2 = 3x - 5$

- Subtract ( 3x ) and add ( 5 ) on both sides of the equation above:

                      $x^2 + ( 4 - 3 ) x + ( 1 + 5 ) = 0\\\\x^2 + x + 6 = 0$

- To solve the quadratic equation we will use the quadratic formula:

                      $x = \frac{-b +/- \sqrt{b^2 - 4ac} }{2a} \\\\x = \frac{-1 +/- \sqrt{1^2 - 4*1*6} }{2} \\\\x = \frac{-1 +/- \sqrt{-23} }{2}$

- We see that the square root of a negative number is "undefined" or have "complex solution". In other words, the solution does not exist.

- The graphs do not intersect.