## anonymous one year ago 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). f(x) = –2(x − 4)^2 + 2 g(x) = 5x^2 − 10x + 7 h(x) = (pictured below)

These are all parabolas that open up or down, so the axis of symmetry is the vertical line$x=x-coordinate~of~vertex$ $$f(x)=-2(x-4)^2+2$$ is in vertex form $$f(x)=a(x-h)^2+k$$. The vertex is $$(h,k)$$ in general, an $$(4,2)$$ for your function. The axis of symmetry is $$x=h$$, or $$x=4$$ for your function. For g(x), you can complete the square and write it in vertex form. Or you can use the formula $$x=-\frac{ b }{ 2a }$$, where a and b come from the coefficients of $$g(x)=ax^2+bx+c$$.