How many real solutions does y = (-x + 4)^2 have?
2 answers:
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.
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.
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ANSWER
The vertex is (-2,1)
EXPLANATION
We want to find the vertex of
We complete the square to obtain,
The first three terms forms a perfect square trinomial.
The vertex form is
This equation is in the form;
where (h,k)=(-2,1) is the vertex.
The vertex is (-2,1)
EXPLANATION
We want to find the vertex of
We complete the square to obtain,
The first three terms forms a perfect square trinomial.
The vertex form is
This equation is in the form;
where (h,k)=(-2,1) is the vertex.