Answer:
![(\frac{1}{2},0),(\frac{3}{2},0)](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B2%7D%2C0%29%2C%28%5Cfrac%7B3%7D%7B2%7D%2C0%29)
Step-by-step explanation:
The vertex form of a parabola is given by:
, where V(h,k) is the vertex of the parabola.
The given parabola has vertex (1,1).
This implies that:
.
Put these values into the vertex form equation.
![\implies y=a(x-1)^2+1](https://tex.z-dn.net/?f=%5Cimplies%20y%3Da%28x-1%29%5E2%2B1)
The y-intercept of this parabola is: (0,-3).
This point lies on the parabola hence it must satisfy its equation.
![\implies -3=a(0-1)^2+1](https://tex.z-dn.net/?f=%5Cimplies%20-3%3Da%280-1%29%5E2%2B1)
![\implies -3=a(-1)^2+1](https://tex.z-dn.net/?f=%5Cimplies%20-3%3Da%28-1%29%5E2%2B1)
![\implies -3=a(1)+1](https://tex.z-dn.net/?f=%5Cimplies%20-3%3Da%281%29%2B1)
![\implies -3=a+1](https://tex.z-dn.net/?f=%5Cimplies%20-3%3Da%2B1)
![\implies -3-1=a](https://tex.z-dn.net/?f=%5Cimplies%20-3-1%3Da)
![\implies -4=a](https://tex.z-dn.net/?f=%5Cimplies%20-4%3Da)
The equation now becomes
![\implies y=-4(x-1)^2+1](https://tex.z-dn.net/?f=%5Cimplies%20y%3D-4%28x-1%29%5E2%2B1)
To find the x-intercept, put y=0 into the equation:
![\implies -4(x-1)^2+1=0](https://tex.z-dn.net/?f=%5Cimplies%20-4%28x-1%29%5E2%2B1%3D0)
![\implies -4(x-1)^2=-1](https://tex.z-dn.net/?f=%5Cimplies%20-4%28x-1%29%5E2%3D-1)
Divide through by -4.
![\implies \frac{-4(x-1)^2}{-4}=\frac{-1}{-4}](https://tex.z-dn.net/?f=%5Cimplies%20%5Cfrac%7B-4%28x-1%29%5E2%7D%7B-4%7D%3D%5Cfrac%7B-1%7D%7B-4%7D)
![\implies (x-1)^2=\frac{-1}{-4}](https://tex.z-dn.net/?f=%5Cimplies%20%28x-1%29%5E2%3D%5Cfrac%7B-1%7D%7B-4%7D)
![\implies (x-1)^2=\frac{1}{4}](https://tex.z-dn.net/?f=%5Cimplies%20%28x-1%29%5E2%3D%5Cfrac%7B1%7D%7B4%7D)
Take plus or minus square root of both sides.
![\implies x-1=\pm \sqrt{\frac{1}{4}}](https://tex.z-dn.net/?f=%5Cimplies%20x-1%3D%5Cpm%20%5Csqrt%7B%5Cfrac%7B1%7D%7B4%7D%7D)
![\implies x-1=\pm \frac{1}{2}](https://tex.z-dn.net/?f=%5Cimplies%20x-1%3D%5Cpm%20%5Cfrac%7B1%7D%7B2%7D)
![\implies x=1\pm \frac{1}{2}](https://tex.z-dn.net/?f=%5Cimplies%20x%3D1%5Cpm%20%5Cfrac%7B1%7D%7B2%7D)
or ![\implies x=1+ \frac{1}{2}](https://tex.z-dn.net/?f=%5Cimplies%20x%3D1%2B%20%5Cfrac%7B1%7D%7B2%7D)
or ![\implies x=1 \frac{1}{2}](https://tex.z-dn.net/?f=%5Cimplies%20x%3D1%20%5Cfrac%7B1%7D%7B2%7D)
Therefore the x-intercepts are:
![(\frac{1}{2},0),(\frac{3}{2},0)](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B2%7D%2C0%29%2C%28%5Cfrac%7B3%7D%7B2%7D%2C0%29)
To the nearest hundredth, we have ![0.50,0),(1.50,0)](https://tex.z-dn.net/?f=0.50%2C0%29%2C%281.50%2C0%29)