Question

Which quadratic function in vertex form can be represented by the graph that has a vertex of (3, 7) and passes through the point (1, -10)?

a) y = -3/4(x + 3)^2 - 7
b) y = -3/4(x - 3)^2 - 7
c) y = 3/4(x + 3)^2 + 7
d) y = 3/4(x - 3)^2 + 7

Answer 1

The quadratic function in vertex form represented by the given graph is y = -17/4(x - 3)^2 + 7.

Step-by-step explanation:

To find the quadratic function in vertex form, we can use the formula y = a(x - h)^2 + k, where (h, k) represents the vertex.

In this case, the vertex is (3, 7).

Plugging these values into the equation, we get y = a(x - 3)^2 + 7.

To determine the value of a, we can use the point (1, -10) that the graph passes through.

Substituting these values, we get -10 = a(1 - 3)^2 + 7, which simplifies to -10 = 4a + 7.

Solving for a, we get a = -17/4.

Therefore, the quadratic function in vertex form represented by the graph is y = -17/4(x - 3)^2 + 7.