Select all the correct answers.Look at the graphs of y = 4x2 + 7x - 11 and y = 3x + 4. At which points are the two equations equal?410-87654327-1y = 3x + 4

Accepted Solution

Answer:Second point (-5/2, -7/2)First point (3/2, 17/2)Step-by-step explanation:We have two equations, and we want to know at wich poin are equal. Hence, we have a system of equations and the solution is nothing more that the point (x,y) where those functions intercepts.4x2+ 7x -11=y3x+4=yLets use substitute method4x2+7x-11=3x+4This can be re arrange as the following eq:4x2+4x-15=0A quadratic equation, its solution can be obtained using the below eq.[tex]x=\frac{-b+/- \sqrt{x^{2}-4ac } }{2a}[/tex]where a=4, b=4, c=-15.Remember, the quadratic equation as a +/- sign, meaning that you will obtain one answer using the + operator and other using the - operator.By doing the above, we have x=-5/2 and x=3/2By using x=3/2 in equation of line (3x+4=y)  we have y=17/2First point (3/2, 17/2)By using x=-5/2 in equation of line (3x+4=y) we have y= -7/2Second point (-5/2, -7/2)Those points are the ones where the line and the parabola intercept.