Quadratic Function

Question

f(x)=(x+9)^2−8

I need to find the domain and range of f. Can someone please help me solve this problem?

Answer 1

The vertex of this upward facing parabola is

(-9,-8)

the domain of all parabolas is all real numbers

the range is y> or = -8

Answer 2

The domain for a quadratic function is always all real numbers; that is -∞ < x < ∞. The range will run from the y coordinate of the vertex up to infinity if the leading coefficient (a) is > 0, or from the y-coordinate of the vertex down to negative infinity if the leading coefficient (a) is < 0.

Your equation is already in the vertex form:

y = a·(x-h)² + k

where (h,k) is the location of the vertex and a is the leading coefficient. Can you find the vertex and leading coefficient of your equation?

Answer 3

f(x) = (x+9)² - 8

The domain of a function, like f(x), is what values you can use for x in the function.

For this function, there is no danger of dividing by zero or taking the square root of a negative number, so the domain is all Real Numbers.

The range of a function, are the values you get evaluating the function for all values of x in the domain.

For this function, looks like all Real Numbers ≥ -8 will be returned as the range. You can verify this by plotting the function.