Question 463805: A quadratic relation has zeros at -2 and 8, and a y-intercept of 8. Determine the equation of the relation in veertex form
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! A quadratic relation has zeros at -2 and 8, and a y-intercept of 8. Determine the equation of the relation in vertex form
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Standard form for parabola: y=A(x-h)^2+k, with (h,k) being the (x,y) coordinates of the vertex.
We have three points to work with: (-2,0),(8,0) and (0,8)
h=midpoint between -2 and 8=(-2+8)/2=6/2=3
equation: y=A(x-3)^2+k
using point (0,8), the y-intercept
8=A(0-3)^2+k
8=9A+k
using point (-2,0), one of the zeros
0=A(-2-3)^2+k
0=25A+k
8=9A+k
subtract
-8=16A
A=-1/2
k=8-9A=8+4.5=12.5
Equation:
y=-.5(x-3)^2+12.5
see graph below as a visual check on the answer
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