Answer:
vertex is (-2,-98)
zeros are (5,0) (-9,0)
y-intercept is (0,-90)
Step-by-step explanation:
we are given
[tex]y=2x^2+8x-90[/tex]
Vertex:
we can use vertex formula
[tex]y=ax^2+bx+c[/tex]
[tex]x=-\frac{b}{2a}[/tex]
we can compare and find a,b and c
a=2 , b=8 and c=-90
so, we can plug it in formula
[tex]x=-\frac{8}{2\times 2}[/tex]
[tex]x=-2[/tex]
now, we can find y-value
[tex]y=2(-2)^2+8(-2)-90[/tex]
[tex]y=-98[/tex]
so, vertex is (-2,-98)
zeros:
we can set y=0
and then we can solve for x
[tex]y=2x^2+8x-90=0[/tex]
we can factor it
[tex]2(x-5)(x+9)=0[/tex]
[tex]x=5,x=-9[/tex]
zeros are
(5,0) (-9,0)
y-intercept:
we can plug x=0 and find y
[tex]y=2(0)^2+8(0)-90[/tex]
[tex]y=-90[/tex]
So, y-intercept is (0,-90)
