A parabola has its vertex at (2, 1) and crosses the x-axis at (1,0) anu al l

the equations below has this parabola for its graph? (TEKS A2.4B-R)

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Ay=1 - (x - 2) ^2

C y = - 1 - (x + 2) ^2

Dy = - 1 - (x - 2) ^2

B

y = 1 + (x + 2) ^2

A

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a (x - h) ² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (2, 1), thus

y = a (x - 2) ² + 1

To find a substitute (1, 0) into the equation

0 = a (1 - 2) ² + 1

0 = a + 1 (subtract 1 from both sides)

a = - 1

Hence

y = - (x - 2) ² + 1 or

y = 1 - (x - 2) ² → A