X2 - 4x + 4 = 0 solve following quadratic equations graphically and a table
1 answer:
Let's create a table, and use arbitrary values of x between -3 and 3 (if the solution is not in this interval, we can use another one later). If we call:
We want to find the x's for with f(x) = 0
This is the table:
And now we can evaluate f(x) in each value of x to complete the table:
The table is:
If we use this values and plot them in the cartesian plane.
We get:
And now if we plot a line that connects the points, we get the graph of the quadratic equation:
Since the problem ask us to find the value of x for which f(x) = 0, we can see both in the table and in the graph that this value is x = 2
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ANSWER
EXPLANATION
Since the parabola has the (0, 0) and the directrix at y=2.
The equation is of the form
where (h,k) is the vertex.
The vertex is half way between the directrix and the focus.
The vertex will be at (0,1)
and is the distance from the vertex to the focus which is 1.