Question

Describe the translation in each function. Then graph the function.

Answer 1

It's a Quadratic that doesn't have any real roots as the parabola doesn't cross the x-axis.

For graphing:

If you're familiar with the parabola of y=x^2, then you could graph that but just translate it upwards by +4 on the y such that f(x)+4 will be equal to it.

If you aren't, then we know the y-intercept is 4, and that's also the point of the minimum point of the curve. If I were you, I'd write a table of some of the integer values:

x y

-2 8

-1 5

0 4

1 5

2 8

The value of y is the same for x and -x as anything squared is positive.This means that there is a line of symmetry in the y-axis.

This then makes it much easier to graph, simply place these points on the graph and make sure the curve is exponential. This means the gradient (steepness) gets greater the bigger the value of x.