x-intercepts: x=5 and x=1 Axis of Symmetry: x=3 Vertex: (3,- 8) Graph:
Practice makes perfect
To graph the quadratic function given in intercept form f(x)=a(x-p)(x-q), we must start by identifying the values of a, p, and q.
f(x)=2(x-5)(x-1)
⇕
f(x)=2(x-5)(x-1)
We can see that a=2, p=5, and q=1. Now, we will follow four steps to graph the function.
Recall that the x-intercepts of a function written in intercept form are the values of p and q. Thus, the points where our function intercepts the x-axis are (5,0) and (1,0).
Finding the Axis of Symmetry
The axis of symmetry is halfway between the x -intercepts, (p,0) and (q,0). Therefore, it has the following equation.
x= p+q2
Since we already know the values of p and q, we can substitute them into the formula.
The axis of symmetry of the parabola is the vertical line with equation x=3. Let's plot the x-intercepts and the axis of symmetry on a coordinate plane.
Calculating the Vertex
The x-coordinate of the vertex is the same as the formula for the axis of symmetry, x= 3. To find the y-coordinate, we need to substitute 3 for x in the given equation.
We found the y -coordinate, and now we know that the vertex is (3,- 8). Let's plot it on our coordinate plane.
Connecting the Points
We can now draw the graph of the function. Since a=2, which is positive, the parabola will open upwards. Let's connect the three points with a smooth curve.
