Question 336452
The general equation for a parabola is {{{y=ax^2+bx+c}}}
Solve for {{{a}}},{{{b}}}, and {{{c}}} using the points ({{{-2}}},{{{2}}}), ({{{0}}},{{{1}}}), and ({{{1}}},{{{2.5}}}). 
{{{ 2=a(-2)^2+b(-2)+c}}}
{{{ 4a-2b+c=2}}}
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{{{ 1=a(0)^2+b(0)+c}}}
{{{ highlight_green(c=1)}}}
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{{{ 5/2=a(1)^2+b(1)+c}}}
{{{ a+b+c=5/2}}}
Simplify with {{{c=1}}}
{{{4a-2b+1=2}}}
1.{{{4a-2b=1}}}
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{{{a+b+1=5/2}}}
{{{a+b=3/2}}}
2.{{{2a+2b=3}}}
Add eq. 1 and eq. 2 to eliminate {{{b}}},
{{{4a-2b+2a+2b=1+3}}}
{{{6a=4}}}
{{{highlight_green(a=2/3)}}}
Then from eq. 3,
{{{2a+2b=3}}}
{{{4/3+2b=9/3}}}
{{{2b=5/3}}}
{{{highlight_green(b=5/6)}}}
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{{{y=(2/3)x^2+(5/6)x+1}}}
Complete the square to put the equation into vertex form,{{{y=a(x-h)^2+k}}} where ({{{h}}},{{{k}}}) is the vertex.
{{{y=(2/3)x^2+(5/6)x+1}}}
{{{y=(2/3)(x^2+(5/4)x)+1}}}
{{{y=(2/3)(x^2+(5/4)x+25/64)+1-(2/3)(25/64)}}}
{{{y=(2/3)(x+5/8)^2+96/96-25/96}}}
{{{y=(2/3)(x+5/8)^2+71/96}}}
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Vertex:({{{-5/8}}},{{{71/96}}})
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{{{drawing(300,300,-5,5,-5,5,circle(-5/8,71/96,0.3),
grid(1),
circle(-2,2,0.3),
circle(0,1,0.3),
circle(1,2.5,0.3),
graph(300,300,-5,5,-5,5,(2/3)x^2+(5/6)x+1))}}}
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The parabola opens upwards.