Write a formula for quadratic function if its graph has the vertex at point ( 1/3 ,−3) and passes through the point (1,1).
1 answer:
Answer:
f(x) = 9(x -1/3)^2 -3
Step-by-step explanation:
In vertex form the equation of a quadratic with vertical scale factor "a" and vertex (h, k) is ...
y = a(x -h)^2 +k
To make the equation have (1, 1) as a solution, we need to find the value of "a". We can put the point coordinates in the equation and solve for "a":
1 = a(1 -1/3)^2 -3 . . . . . for (h, k) = (1/3, -3) as given
1 = (4/9)a -3 . . . . simplify
4 = (4/9)a . . . . . . add 3
9 = a . . . . . . . . . . multiply by 9/4
The quadratic function you desire is ...
f(x) = 9(x -1/3)^2 -3
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. It is a third degree polynomial with a leading coefficient of -2.
Answer:
Option 1 is correct.
Step-by-step explanation:
The given polynomial is
we have to find all the rational roots of the polynomial f(x)
The Rational Root Theorem states that the all possible roots of a polynomial are in the form of a rational number i.e in the form of
where p is a factor of constant term and q is the factor of coefficient of leading term.
In the given polynomial the constant is -12 and the leading coefficient is 20.
So, the all possible rational roots of the given polynomial are,
Now, the rational roots of polynomial satisfy the given polynomial
Hence, rational root.
rational root
not a rational root.
hence, option 1 is correct