HELP TRANSLATED GRAPH EXPRESSION

Question

The function h is defined as follows h(x)=-4x^2+7. If the graph of h is translated vertically downward by 6 units, it becomes the graphs of a function g. Find the expression for g(x).

Answer 1

When you translate a graph vertically, every point on the graph moves by the specified amount. H9x) = y. If you can make the y intercept 6 units below the current value you will have your answer.

y = 4x² + 7. Set x = 0; h(0) = 7 so the y-intercept of h(x) is 7. Translating 6 down, subtract 6 from 7 this gives a new y-intercept of 7-6=1. So g(x) = 4x² + 1

You can verify this by putting in a few values of x in h(x) and g(x). for a given x, g(x) should always be 6 less than h(x).