Question 389432: Find the x-intercepts of the parabola with vertex (1,1) and y-intercepts (0,-3).
Found 2 solutions by ewatrrr, lwsshak3:
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website!
Hi,
the vertex form of a parabola,  where(h,k) is the vertex
vertex (1,1)
y =a(x-1)^2 +1
using y-intercept pt(0,3) to find a
3 = a(-1)^2 + 1
2 = a
y = 2(x-1)^2 + 1 OR y = 2[x^2 - 2x +1] + 1
Vertex Pt(1,1) in the minimum point for the parabola (a>0)
parabola does not intercept the x-axis
Answer by lwsshak3(11628)  (Show Source):
You can put this solution on YOUR website! The parabola can be defined by the form:
y=A(x-h)^2+k, h,k representing the (x,y) coordinates of the vertex
with the given y-intercept coordinates (0,-3) and vertex coordinates(1,1)
-3=A(0-1)^2+1
A=-4
equation of parabola: y=-4(x-1)^2+1
=-4(X^2-2x+1)+1 =-4x^2+8x-3
to find x-intercept, set y=0
0=-4(x-1)^2+1
4(x-1)^2=1
(x-1)^2=1/4
taking sqrt of both sides,
x-1=±1/2
x=1/2 or 3/2
ans: x -intercepts at 1/2 and 3/2
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