Quadratic function rules can be expressed in factored form, sometimes referred to as intercept form.
From the graph, the following characteristics can be connected to the function rule.
Points on the parabola with the same y-coordinate are equidistant from the axis of symmetry. That means, the axis of symmetry is located halfway between the zeros. Notice that the zeros lie 6 units apart.
Considering the direction of the parabola, given by the a-value in the function rule, the shape of the graph can be seen. Here, a=-1. Thus, the parabola opens downward. To draw the parabola, connect the points with a smooth curve.
Allister and Lebowski spend a Sunday afternoon launching bottle rockets in their backyard. For one round of launches, they collect the following data. The trajectory of Allister's rocket can be modeled by the function A(x)=-x(x−3), while Lewbowski's is modeled by L(x)=-2x2+6x. Note that x and y are both given in meters. The graph of L is shown.
Determine whose rocket went higher and whose went further.
Here, we will compare two quadratic functions that model the trajectory of each rocket. To find the maximum height we'll need the vertex, and to find the horizontal distance we'll need the zeros. We'll begin with Lebowski's rocket.