Answer:
The x-intercepts are
(x1,y1)=(4,0)
(x2,y2)=(6,0)
Step-by-step explanation:
we know that
The equation of the given parabola is
[tex](y-k)=a(x-h)^{2}[/tex]
we have
the vertex is the point (5,-4)
substitute
[tex](y+4)=a(x-5)^{2}[/tex]
The y-intercept is the point (0,96)
substitute and solve for a
[tex](96+4)=a(0-5)^{2}[/tex]
[tex]100=a(25)[/tex]
[tex]a=100/25=4[/tex]
The equation of the vertical parabola is equal to
[tex](y+4)=4(x-5)^{2}[/tex]
Find the x-intercepts
Remember that
The x-intercepts are the values of x when the value of y is equal to zero
For y=0
[tex]4=4(x-5)^{2}[/tex]
Simplify
[tex]1=(x-5)^{2}[/tex]
Rewrite
[tex](x-5)^{2}=1[/tex]
square root both sides
[tex](x-5)=(+/-)1[/tex]
[tex]x=(+/-)1+5[/tex]
[tex]x=(+)1+5=6[/tex]
[tex]x=(-)1+5=4[/tex]
therefore
The x-intercepts are
(x1,y1)=(4,0)
(x2,y2)=(6,0)
