Question 1053671
The graph gives five points but the symmetry axis and vertex are not clear, so too difficult to read graphically.  Your given equation form has two unknown constants, a and b.  You can choose any two points from the graph, but NOT both zeros at the same time.


{{{ax^2+bx-4=y}}}


NOTE:  I am picking points from the graph and looking for resulting useful equations to help solve for a and b:


{{{a*0^2+b*0-4=-4}}}, that point gives us nothing.


{{{a*1^2+b*1-4=0}}}
{{{a+b=4}}}-----may be useful


{{{a*2^2+b*2-4=2}}}
{{{4a+2b=6}}}
{{{2a+b=3}}}----------useful and now should be enough


SOLVE THIS SYSTEM:
{{{system(a+b=4,2a+b=3)}}}
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{{{a=3-4}}}
{{{a=-1}}}
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{{{b=3-2a}}}
{{{b=3-2(-1)}}}
{{{b=5}}}
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{{{highlight(y=-x^2+5x-4)}}}