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Sloan [31]
3 years ago
14

Hurry plz answer The y-intercept of a parabola is 1, and its vertex is at (1,0). What function does the graph represent?

Advanced Placement (AP)
1 answer:
Wewaii [24]3 years ago
6 0

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>

<em></em>

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)

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