To solve this problem you must apply the proccedure shown below:
1. You have that the standard form of the equation for a parabola is:
[tex] y=a(x-h)^{2}+k [/tex]
Where [tex] (h,k) [/tex] is the vertex
2. Substitute the values shown into the equation:
[tex] y=a(x-1)^{2} -17 [/tex]
3. Now, substitute [tex] y=-16 [/tex] and [tex] x=0 [/tex] to calculate [tex] a [/tex]:
[tex] -16=a(0-1)^{2} -17\\ a=1 [/tex]
4. Then, the equation of the parabola is:
[tex] y=(x-1)^{2} -17 [/tex]
5. To calculate the x-intecept [tex] y [/tex] must be [tex] y=0 [/tex]. Substitute it into the equation and solve for [tex] x [/tex]:
[tex] 0=(x-1)^{2} -17\\ x^{2} -x-16=0\\ x=4.53; x=-3.53
[/tex]
The answer is: [tex] (4.53,0),(-3.53,0) [/tex]
