question 1- explain how Sheldon immediately knew howard was incorrect? question 2- identify where Howard made a mistake in his work?​

Answer:Part 1) In the procedurePart 2) In the procedureStep-by-step explanation:Part 1) Observing the graphThe roots are x=-1/2 and x=4Remember that, the roots are the x-values when the value of y is equal to zero (the x-intercepts)That's why Sheldon immediately realizes Howard's solution is incorrectPart 2) we have[tex]y=2x^{2}-7x-4[/tex]The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to [tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex] in this problem we have equate the equation to zero[tex]2x^{2}-7x-4=0[/tex]  so [tex]a=2\\b=-7\\c=-4[/tex] substitute[tex]x=\frac{-(-7)(+/-)\sqrt{-7^{2}-4(2)(-4)}} {2(2)}[/tex] [tex]x=\frac{7(+/-)\sqrt{49+32}} {4}[/tex] Howard's error is in this step, is wrong with the sign of the number 7, is positive instead of negative[tex]x=\frac{7(+/-)\sqrt{81}}{4}[/tex] [tex]x=\frac{7(+/-)9}{4}[/tex] [tex]x=\frac{7(+)9}{4}=4[/tex] [tex]x=\frac{7(-)9}{4}=-1/2[/tex]