Graph the function. how is the graph a translation of f(x) = x2? y = (x –1)2 + 3 a. f(x) translated down 3 unit(s) and translated to the right 1 unit(s) b. f(x) translated down 3 unit(s) and translated to the left 1 unit(s) c. f(x) translated up 3 unit(s) and translated to the left 1 unit(s) d. f(x) translated up 3 unit(s) and translated to the right 1 unit(s)

ANSWER

The correct answer is D.

EXPLANATION

The function given to us to graph is

This function is written in the form

Where is the vertex.

By comparing to the given function,

The coordinates of the vertex are

.

Also , the graph opens up.

We also need to determine the x and y intercepts.

At x-intercept

We need to take the square of both sides. But square root of negative 3 gives an imaginary number. This means the graph will be hanging. It won't touch the x-axis.

At y-intercept

The y-intercept is .

We can now use the above information to graph the function as shown in the attachment.

We can see from the graph that is obtained when the graph of is shifted up 3 units and to the right 1 unit.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4