Answer:

To write each function in standard form, we need to expand and simplify the expressions:

1. f(x) = x^2 - 10

Expanding:

f(x) = x^2 - 10

This is already in standard form, as it is a quadratic function in the form of ax^2 + bx + c.

2. f(x) = x^2 - 3

Expanding:

f(x) = x^2 - 3

This is also already in standard form, as it is a quadratic function in the form of ax^2 + bx + c.

To determine the vertex of each graph, we can use the vertex formula:

For a quadratic function in the form of f(x) = ax^2 + bx + c, the vertex can be found using the formula:

x = -b / (2a)

y = f(x)

Let's apply this formula to each function:

1. f(x) = x^2 - 10

a = 1 (coefficient of x^2)

b = 0 (coefficient of x)

c = -10

x = -b / (2a) = -0 / (2 * 1) = 0

y = f(0) = (0)^2 - 10 = -10

The vertex of the graph is (0, -10).

2. f(x) = x^2 - 3

a = 1 (coefficient of x^2)

b = 0 (coefficient of x)

c = -3

x = -b / (2a) = -0 / (2 * 1) = 0

y = f(0) = (0)^2 - 3 = -3

The vertex of the graph is (0, -3).