Answer:
[tex]y=-2x^2 -16x -28[/tex]
Step-by-step explanation:
We are given with the graph of a parabola
[tex]y=-2x^2 + 3x -5[/tex]
a=-2, b=3 and c=-5
Discriminant = [tex]b^2-4ac= 3^2 -4(-2)(-5)= 9-40= -31[/tex]
Discriminant is negative so x intercepts are imaginary.
In the graph we have two x intercepts.
[tex]y=-2x^2 -4x -2[/tex]
a=-2, b=-4 and c=-2
Discriminant = [tex]b^2-4ac= (-4)^2 -4(-2)(-2)=0[/tex]
Discriminant is 0 so there is only one x intercept
[tex]y=-2x^2 -16x -28[/tex]
a=-2, b=-16 and c=-28
Discriminant = [tex]b^2-4ac= (-16)^2 -4(-2)(-28)=32[/tex]
Discriminant is positive so there are two x intercepts
[tex]x=\frac{-b+-\sqrt{b^2-4ac} }{2a} =\frac{16+-\sqrt{32} }{2(-2)}[/tex]
We will get two values for x
x= -5.414 , x=-2.586
Two x intercepts are negative . That is the x intercepts of given graph.
[tex]y=-2x^2 +16x -28[/tex]
a=-2, b=16 and c=-28
Discriminant = [tex]b^2-4ac= (16)^2 -4(-2)(-28)=32[/tex]
Discriminant is positive so there are two x intercepts
