Question

Three functions are given below: f(x), g(x), and h(x). Explain how to find the axis of symmetry for each function, and rank the functions based on their axis of symmetry (from smallest to largest; x=1 would be smaller than x=5). f(x) g(x) h(x) f(x) = (x + 4)2 + 1 g(x) = 2x2 − 16x + 15 graph of 2 times the quantity of x minus 1 squared, minus 3.

A. Ranking the functions from largest to smallest axis of symmetry.
B. Ranking the functions based on a different property, such as the vertex or the range.
C. Providing an incorrect explanation for how to find the axis of symmetry.

Answer 1

The axis of symmetry for quadratic functions is found using the formula x = -b/(2a). f(x) has an axis of symmetry at x = -4, h(x) at x = 1, and g(x) at x = 4, ranked from smallest to largest.

Step-by-step explanation:

To find the axis of symmetry for the given quadratic functions, we need to use the formula x = -b/(2a), where a and b are the coefficients of x^2 and x respectively. For the function f(x) = (x + 4)^2 + 1, the axis of symmetry is x = -4 because the vertex form of the function gives the axis directly. For g(x) = 2x^2 − 16x + 15, the axis of symmetry can be found using the formula, giving x = 16/(2*2) = 4. Lastly, the graph of h(x) = 2(x - 1)^2 - 3 reveals the axis of symmetry to be x = 1.

Ranking the functions from smallest to largest axis of symmetry:

1. f(x) with an axis of symmetry at x = -4
2. h(x) with an axis of symmetry at x = 1
3. g(x) with an axis of symmetry at x = 4