By finding the x-coordinate of each vertex, we will see that the correct options are C and E.
How to identify the x-value of the vertex?
For a quadratic equation of the form:
y = (x - a)*(x - b)
Where a and b are the roots, such that a < b, the x-value of the vertex is given by:
a + (b - a)/2
With that, we can check the x-value of the vertex of each option.
A) y=(x-2)(x-4)
The x-value of the vertex is:
2 + (4 - 2)/2 = 3
B) y=(x-2)(x+2)
The x-value of the vertex is:
-2+ (2 - (-2))/2 = 0
C) y=(x-1)(x-3)
The x-value of the vertex is:
1 + (3 - 1)/2 = 2
D) y = x(x+4) = (x - 0)*(x + 4)
The x-value of the vertex is:
-4 + (0 - (-4))/2 = -2
E) y=x(x-4) = (x - 0)*(x - 4)
The x-value of the vertex is:
4 + (0 - (4))/2 = 2
So the two options that have a vertex with x-coordinate 2 are options C and E.
If you want to learn more about quadratic equations, you can read:
https://brainly.com/question/1214333
