x-intercepts: x=- 6 and x=- 2 Axis of Symmetry: x=- 4 Vertex: (- 4,- 12) Graph:
Practice makes perfect
To graph the quadratic function given in intercept form f(x)=a(x-p)(x-q), we must start by identify the values of a, p, and q.
y=3(x+2)(x+6)
⇕
y=3(x-(- 2))(x-(- 6))
We can see that a=3, p=- 2, and q=- 6. 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 (- 2,0) and (- 6,0).
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=- 4. 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=- 4. To find the y-coordinate, we need to substitute - 4 for x in the given equation.
We found the y -coordinate, and now we know that the vertex is (- 4,- 12). Let's plot it on our coordinate plane.
Connecting the Points
We can now draw the graph of the function. Since a=3, which is positive, the parabola will open upwards. Let's connect the three points with a smooth curve.
