Answer:
Option A. The function f(x) = (x − 1)2 has a y-intercept of 1 and its vertex at (1, 0)
Explanation:
If the <em>y-intercept</em> represents the value of<em> 'y'</em> when <em>x=0. </em>
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Let's evaluate each option:
A. f(x) = (x − 1)2 = (0 − 1)2 = 1
B. f(x) = (x + 1)2 = (0 + 1)2 = 1
C. f(x) = -1(x − 1)2 = -1(0 − 1)2 = -1
D. f(x) = -1(x + 1)2= -1(0 + 1)2 = -1
So only Options 'A' and 'B' has a y-intercept of 1. Options 'C' and 'D' are discarded.
Now, The vertex of a parabola is the highest or lowest point of a parabola.
The vertex form of the equation of a parabola is: y = a(x-h)2 + k, where (h, k) is the vertex point.
Then, one function with a vertex at (1, 0) should look like the following:
y = a(x-1)2.
Clearly, the option 'A' is the correct option. The function f(x) = (x − 1)2 has a y-intercept of 1 and its vertex at (1, 0)
