How many real solutions does y = (-x + 4) ^2 have?

Short answer 1

Comment

There are a couple of ways of doing this to show there there is just one solution. The most easily done way is to graph the quadratic. I have done that for you.

Notice that the quadratic touches the x axis, it does not cut it in two places or no places. When a quadratic just touches the x axis, it has only one solution.

Method 2

The quadratic is shown in the vertex form. If there was a number outside he bracket showing squares then you would get

y = (-x + 4) ^2 + 4 (drawn in blue)

y = (-x + 4) ^2 - 6 (drawn in green)

These two examples show what the vertex form would look like if the axis was cut in 2 places or no places and there would be no solution for the first one and 2 places for the second one.

It has 2 solutions

1. y = - 1

2. y = 4/3 = 1.333