Identify the x-intercepts first. Then use it to find the axis of symmetry.
x-intercepts: x=- 1 and x=- 5 Axis of Symmetry: x=- 3 Vertex: (- 3,4) 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)=-(x+1)(x+5)
⇕
f(x)=-1(x-(-1))(x-(-5))
We can see that a=-1, p=-1, and q=-5. 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. Therefore, the points where our function intercepts the x-axis are (-1,0) and (-5,0).
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 (- 3,4). 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.
