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taten1701
26.05.2021 •
Mathematics
Systems of equations auto repair problem
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Ответ:
Step-by-step explanation:
to understand thisyou need to know about:quadratic functionPEMDASlet's solve:vertex:(h,k)
therefore
vertex:(-1,4)
axis of symmetry:x=h
therefore
axis of symmetry:x=-1
to find the quadratic equation we need to figure out the vertex form of quadratic equation and then simply it to standard form i.e ax²+bx+c=0vertex form of quadratic equation:
y=a(x-h)²+ktherefore
y=a(x-(-1))²+4y=a(x+1)²+4it's to notice that we don't know what a is
therefore we have to figure it out
the graph crosses y-asix at (0,3) coordinates
so,
3=a(0+1)²+4
simplify parentheses:
simplify exponent:
therefore
our vertex form of quadratic equation is
y=-(x+1)²+4let's simplify it to standard form
simplify square:
simplify parentheses:
simplify addition:
therefore our answer is D)y=-x²-2x+3
the domain of the function
and the range of the function is
zeroes of the function:
factor out x and -1 respectively:
group:
therefore