Identify the x -intercepts first. Then use it to find the axis of symmetry.
x-intercepts: x=- 7 and x=0 Axis of Symmetry: x=- 3.5 Vertex: (- 3.5,49) 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.
y=-4 x(x+7)
⇕
y=- 4(x- )(x-(- 7))
We can see that a=- 4, p= , and q=- 7. 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 (- 7,0).
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=- 3.5. 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= - 3.5. To find the y -coordinate, we need to substitute - 3.5 for x in the given equation.
We found the y-coordinate, and now we know that the vertex is (- 3.5,49). Let's plot it on our coordinate plane.
Connecting the Points
We can now draw the graph of the function. Since a=- 4, which is negative, the parabola will open downwards. Let's connect the three points with a smooth curve.
