Answer:
d) y = (-3/4)(x - 3)^2 - 7
Explanation:
The vertex form of a quadratic function is:
y = a(x - h)^2 + k
where (h, k) is the vertex of the parabola.
We are given that the vertex is (3, -7), so we can substitute these values into the equation:
y = a(x - 3)^2 - 7
Now we need to find the value of "a". We can use the fact that the function passes through the point (1, -10). Substituting these values into the equation gives us:
-10 = a(1 - 3)^2 - 7
Simplifying, we get:
-10 = 4a - 7
-3 = 4a
a = -3/4
Substituting this value of "a" into the equation, we get:
y = (-3/4)(x - 3)^2 - 7
Therefore, the quadratic function in vertex form that can be represented by the graph that has a vertex at (3, -7) and passes through the point (1, -10) is:
y = (-3/4)(x - 3)^2 - 7