To solve the by graphing, we will draw the graph of the and the on the same . Let's start with the .
Graphing the Parabola
To graph the parabola, we first need to identify
For this equation we have that
Now, we can find the using its formula. To do this, we will need to think of
as a function of
Let's find the
coordinate of the vertex.
We will use the
coordinate of the vertex to find its
coordinate by substituting it into the given equation.
coordinate of the vertex is
Thus, the vertex is the point
With this, we also know that the of the parabola is the line
Next, let's find two more points on the curve, one on each side of the axis of symmetry.
Both and are on the graph. Let's form the parabola by connecting these points and the vertex with a smooth curve.
Graphing the Line
Let's now graph the linear function on the same coordinate plane. For a linear equation written in , we can identify its slope and -intercept
The slope of the line is and the intercept is
Finding the Solutions
Finally, let's try to identify the coordinates of the of the parabola and the line.
It looks like the only point of intersection occurs at
To check our answer, we will substitute the coordinates of the point of intersection in both equations of the system. If they produce true statements, our solution is correct.
Equation (I) and Equation (II) both produced true statements. Therefore,
is a correct solution.