We have a , written in . To draw the graph of the related we must start by identifying the values of and
We can see that and Now, we will follow four steps to graph the function.
- Find the .
- Calculate the .
- Identify the and its across the axis of symmetry.
- Connect the points with a .
Finding the Axis of Symmetry
The axis of symmetry is a with equation
Since we already know the values of
we can substitute them into the formula.
The axis of symmetry of the parabola is the vertical line with equation
Calculating the Vertex
To calculate the vertex, we need to think of
as a function of
We can write the expression for the vertex by stating the
coordinates in terms of
Note that the formula for the
coordinate is the same as the formula for the axis of symmetry, which is
coordinate of the vertex is also
To find the
coordinate, we need to substitute
in the given equation.
We found the
coordinate, and now we know that the vertex is
Identifying the intercept and its Reflection
The intercept of the graph of a quadratic function written in standard form is given by the value of Thus, the point where our graph intercepts the axis is Let's plot this point and its reflection across the axis of symmetry.
Connecting the Points
We can now draw the graph of the function. Since which is positive, the parabola will open upwards. Let's connect the three points with a smooth curve.
By looking at the graph, we can state approximated values for the intercepts. We can see that the parabola intercepts the axis at and approximately.