Question 524018
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)
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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
{{{ graph( 300, 300, -10, 10, -10, 10,-x^2/20+5) }}} 
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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
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See graphs below:
{{{ graph( 300, 300, -10, 10, -10, 10,-2x^2+4) }}}