Answer:
[tex]y=-x^2+8x-13[/tex]
Step-by-step explanation:
The standard form of a quadratic equation is:
[tex]y=ax^2+bx+c[/tex]
so to rewrite the equation in this form we do the following steps:
[tex]y=-(x-4)^2+3[/tex]
First we apply the formula [tex]( a-b)^2 = a^2 -2ab + b^2\\[/tex]
so now the equation becomes,
[tex]y=-(x-4)^2+3\\y=-((x)^2-2(x)(4)+(4)^2)+3\\y=-(x^2-8x+16)+3\\y=-x^2+8x-16+3\\y=-x^2+8x-13\\y=ax^2+bx+c\\[/tex]
now if we compare the equation that we got with our standard form it is in the exact format thus the value of a = -1 , b = 8 and c = -13
