Start with f(x)=x^2. In vertex form this is 1(x-0)^2+0.
- Translating up 7 units adds 7 to the constant term (k).
- So g(x)=1(x-0)^2+7.
Simplified, g(x)=x^2+7. Thus in the form a(x-h)^2+k: a=1, h=0, k=7.
Step-by-step: translate the parabola f(x)=x^2 up 7 units and express g(x) in vertex form a(x-h)^2+k. Clear algebraic reasoning for students learning transformations of quadratic functions.
Start with f(x)=x^2. In vertex form this is 1(x-0)^2+0.
Simplified, g(x)=x^2+7. Thus in the form a(x-h)^2+k: a=1, h=0, k=7.