Answer:
Part A: check B, E and F.
Part B: check E and G.
Step-by-step explanation:
The equation [tex]y = a(x - b)^2 + c[/tex] is the equation of a parabola written in the vertex form, where the vertex will be (b, c).
So, if the vertex is (2, -1), we have that b = 2 and c = -1
To find the c value, we use the information that the y-intercept is 3, so we have the point (0, 3). Using x = 0 and y = 3, we have:
[tex]3 = a(0 - 2)^2 - 1[/tex]
[tex]3 = 4a - 1[/tex]
[tex]4a = 4[/tex]
[tex]a = 1[/tex]
So we have a = 1, b = 2 and c = -1.
Part A: check B, E and F.
To find the x-intercepts, we need to find the values of x where y = 0:
[tex]0 = (x - 2)^2 - 1[/tex]
[tex]x^2 - 4x + 4 - 1 = 0[/tex]
[tex]x^2 - 4x + 3 = 0[/tex]
Solving using Bhaskara's formula (a = 1, b = -4 and c = 3), we have:
[tex]\Delta = b^2 - 4ac = 16 - 12 = 4[/tex]
[tex]x_1 = (-b + \sqrt{\Delta})/2a = (4 + 2)/2 = 3[/tex]
[tex]x_2 = (-b - \sqrt{\Delta})/2a = (4 - 2)/2 = 1[/tex]
So the x-intercepts are 1 and 3
Part B: check E and G.
