Respuesta :
Answer:
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) = (1, 0) , thus
y = a(x - 1)² + 0
To find a substitute the coordinates of the y- intercept (0, 1) into the equation
1 = a(- 1)² = a , thus
a = 1
y = (x - 1)² → A
Considering it's y-intercept and vertex, the equation of the parabola is given by:
[tex]y = (x - 1)^2[/tex]
What is the equation of a parabola given it’s vertex?
The equation of a quadratic function, of vertex (h,k), is given by:
[tex]y = a(x - h)^2 + k[/tex]
In which a is the leading coefficient.
In this problem, the vertex is (1,0), hence h = 1, k = 0 and:
[tex]y = a(x - 1)^2[/tex]
The y-intercept is of 1, hence, when x = 0, y = 1, so:
[tex]y = a(x - 1)^2[/tex]
[tex]1 = a(0 - 1)^2[/tex]
[tex]a = 1[/tex]
Hence, the equation is:
[tex]y = (x - 1)^2[/tex]
More can be learned about the equation of a parabola at https://brainly.com/question/24737967
