Question 524018: Help please!!!
I have to write an equation in vertex form for two parabolas.
first has vertex at (0,5) and point (10,0)
second has vertex at (0,4) and point (1,2)
Thank you so much.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! I have to write an equation in vertex form for two parabolas.
first has vertex at (0,5) and point (10,0)
second has vertex at (0,4) and point (1,2)
**
Standard form of equation for parabola: y=A(x-h)^2+k, (h,k) being the (x,y) coordinates of the vertex, A=multiplier which affects steepness or slope of the curve.
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For vertex (0,5) and point (10,0)
Equation: y=A(x-0)^2+5=Ax^2+5
solving for A, using coordinates of point (10,0)
0=A(10^2)+5
-5=100A
A=-5/100=-1/20
Equation: y= -x^2/20+5
see graph below as a visual check
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For vertex (0,4) and point (1,2)
Equation: y=A(x-0)^2+4=Ax^2+4
solving for A, using coordinates of point (1,2)
2=A(1^2)+4
-2=(1)A
A=-2
Equation: y=-2x^2+4
..
See graphs below:
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