Question

Which quadratic function has its vertex at (2,3) and passes through (2,3)?

a)\(y^2(x - 2)^2 + 3)
b) (y = 3(x + 2) + 3)
c) (y = -3(x - 2)^2 - 3)
d) (y = 2(x - 2)^2 - 3)

Answer 1

The quadratic function that has its vertex at (2,3) and passes through (2,3) is y = 2(x - 2)^2 - 3.

Step-by-step explanation:

The correct option is d) (y = 2(x - 2)^2 - 3)

To determine the quadratic function that has its vertex at (2,3) and passes through (2,3), we can use the vertex form of a quadratic equation, which is y = a(x - h)^2 + k, where (h, k) represents the vertex coordinates.

In this case, h = 2 and k = 3, so the equation becomes y = a(x - 2)^2 + 3. To find the value of a, we can substitute the coordinates of the given point (2,3) into the equation. Since the y-coordinate is already 3, we have 3 = a(2 - 2)^2 + 3. Solving for a, we find that a = 2.

Therefore, the quadratic function with a vertex at (2,3) and passing through (2,3) is y = 2(x - 2)^2 - 3.