Question

All help on this following problem would be greatly appreciated!

Identify the vertex, axis of symmetry, maximum or minimum, and domain and range of the following function.

f(x) = 2 (x + 9)² − 4

Answer 1

The equation is written in vertex form. This lets you read the answers to the questions from the equation by matching it to the pattern ...

... y = a(x -h)² +k

where (h, k) is the vertex, and the sign of "a" tells you whether the curve opens upward or downward.

In your equation, a=2, h= -9, k= -4.

This means the vertex is (-9, -4).

The axis of symmetry is the vertical line through the vertex, x = -9.

The sign of "a" is positive, meaning the curve opens upward and the vertex is a minimum (the low end of the range).

As with all polynomials, the domain is all real numbers.

The y-value at the vertex is -4, so the range is all real numbers greater than or equal to -4.