x-intercepts: x=- 6 and x=0 Axis of Symmetry: x=- 3 Vertex: (- 3,9) 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.
g(x)=- x(x+6)
⇕
g(x)=- 1(x- )(x-(- 6))
We can see that a=- 1, p= , 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 ( ,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=- 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 (- 3,9). Let's plot it on our coordinate plane.
Connecting the Points
We can now draw the graph of the function. Since a=- 1, which is negative, the parabola will open downwards. Let's connect the three points with a smooth curve.
