Question

Can someone help me please. I'm desperate I can get halfway through but I can't figure it out 100%..

Find the x-intercepts of the parabola with vertex (4,-1) and y-intercept (0,15). Answer in this form: (x1,y1),(x2,y2)

Answer 1

vertex is \((4,-1)\) so you know it looks like
\[y=a(x-4)^2-1\] and we can solve for \(a\) because we know that if \(x=0\) then \(y=15\) so set
\[15=a(0-4)^2-1\]
\[15=16a-1\]
\[16a=16\]
\[a=1\]

Answer 2

so your parabola has the equation
\[y=(x-4)^2-1\] now you can set it equal to zero and solve

Answer 3

\[(x-4)^2-1=0\]
\[(x-4)^2=1\]
\[x-4=1\] or
\[x-4=-1\]

\[x=5\] or \[x=3\]

Answer 4

Trying it right now

Answer 5

OH MY GOODNESS THANK YOU SO MUCH! <3