which function has a vertex on the y - axis?\n○ (f(x)=(x - 2)^2)\n○ (f(x)=x(x + 2))\n○ (f(x)=(x - 2)(x +…
which function has a vertex on the y - axis?\n○ (f(x)=(x - 2)^2)\n○ (f(x)=x(x + 2))\n○ (f(x)=(x - 2)(x + 2))\n○ (f(x)=(x + 1)(x - 2))
Answer
Explanation:
Step1: Recall vertex - form of a quadratic function
The vertex - form of a quadratic function is (y = a(x - h)^2+k), where the vertex is ((h,k)). If the vertex is on the (y) - axis, then (h = 0).
Step2: Expand each function
- For (f(x)=(x - 2)^2=x^{2}-4x + 4), in vertex - form (y=(x - 2)^2+0), the vertex is ((2,0)).
- For (f(x)=x(x + 2)=x^{2}+2x). Completing the square: (y=x^{2}+2x=(x + 1)^2-1), the vertex is ((-1,-1)).
- For (f(x)=(x - 2)(x + 2)=x^{2}-4). In vertex - form (y=(x-0)^2-4), the vertex is ((0,-4)).
- For (f(x)=(x + 1)(x - 2)=x^{2}-x-2). Completing the square: (y=x^{2}-x-2=(x-\frac{1}{2})^{2}-\frac{1}{4}-2=(x-\frac{1}{2})^{2}-\frac{9}{4}), the vertex is ((\frac{1}{2},-\frac{9}{4})).
Answer:
(f(x)=(x - 2)(x + 2))