The function's standard form equation is equivalent to [tex]\frac{-x^2}{4}+1=0[/tex].
A mathematical expression (equation) that can be used to define and represent the relationship between two or more variables on a graph is known as a quadratic function.
The standard form of a quadratic equation in mathematics is given by;
[tex]ax^2+bx+c=0\\y=f(x)=ax^2+bx+c[/tex]
Next, using the information in the previous table, we would create the following system of equations:
[tex]-3=a(-4)^2+b(-4)+c\\-3=16a-4b+c[/tex].......equation (i)
[tex]0=a(-2)^2+b(-2)+c\\0= 4a-2b+c[/tex]........equation(ii)
[tex]1=a(0)^2+b(0)+c\\1=c[/tex].........equation (iii)
Inputting the value of c into equations 1 and 2 results in:
[tex]-4=16a-4b[/tex]......ewuation(iv)
[tex]-1=4a-2b[/tex]......equation(v)
Equation 5 is multiplied by two and solved concurrently to yield:
[tex]-2=8a\\a=\frac{-2}{8} \\a=\frac{-1}{4}[/tex]
What we have for b's value is:
[tex]-1=4a-2b\\-1=4(\frac{-1}{4})-2b\\ -1=-1-2b\\2b=0\\b=0[/tex]
Inputting the values of a, b, and c into a quadratic equation in standard form:
[tex]ax^2+bx+c=0\\\frac{-1}{4}x^2+(0)x+1=0\\ \frac{-x^2}{4} +1=0[/tex]
When x equals 2, we get:
[tex]\frac{-x^2}{4} +1=0\\\frac{-2^2}{4}+1=0\\ \frac{-4}{4}+1=0\\ -1+1=0[/tex]
To learn more about quadratic function, refer:-
https://brainly.com/question/18958913
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