Which function in vertex form is equivalent to f(x) = x2 + x +1?
A). f(x) = (x + one-quarter) squared + three-quarters
B). f(x) = (x + one-quarter) squared + five-quarters
C). f(x) = (x + one-half) squared + three-quarters
D). f(x) = (x + one-half) squared + five-quarters
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Answers
Step-by-step explanation:
the answer of this question is (C)
Concept:
Equations of type f(x) = ax² + bx + c = 0 of degree 2 in one variable, where a, b, c, and an are all nonzero. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f. (x). The roots of the quadratic equation are the values of x that fulfil the equation (α,β).
It is a given that the quadratic equation has two roots. Roots might have either a true or imaginary nature.
Given:
f(x) = x² + x +1
Find:
Which function in vertex form is equivalent to f(x) = x2 + x +1?
A). f(x) = (x + one-quarter) squared + three-quarters
B). f(x) = (x + one-quarter) squared + five-quarters
C). f(x) = (x + one-half) squared + three-quarters
D). f(x) = (x + one-half) squared + five-quarters
Solution:
f(x) = x² + x +1
f(x)=x²+2x1/2x1x +1/4-1/4+1
=(x+1/2)²+3/4
So the answer is option C f(x) = (x + one-half) squared + three-quarters
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