Objective: Graph quadratic equations and identify the intercepts, vertex, and axis of symmetry of a parabola.
The graph of a quadratic equation (which has the form y = ax2 + bx + c) is a parabola, which is a curve that is symmetric about a vertical line called the axis of symmetry. The point at which a parabola intersects the axis of symmetry is called the vertex, and is the point at which the equation has either its minimum or its maximum y-value. An equation in which a>0 produces a parabola that "opens upward" and therefore the vertex is a minimum point. An equation in which a<0 produces a parabola that "opens downward" and therefore the vertex is a maximum point. The video below shows some examples of parabolas and explains how to graph a quadratic equation by generating a table of ordered pairs.
In order to graph a quadratic equation without generating a table of ordered pairs, it is possible to quickly determine key features of the parabola including its intercepts, vertex, and axis of symmetry. The y-intercept of a parabola can be found by setting x=0 and solving the equation for y. The x-intercept(s) of a parabola can be found by setting y=0 and solving the resulting quadratic equation for x. Since a quadratic equation can have zero, one, or two solutions, a parabola can have zero, one, or two x-intercepts. To identify the coordinates of the vertex, it is helpful to first determine the equation for the axis of symmetry using the formula x = -b/2a. The x-coordinate of the vertex can then be found from the axis of symmetry, and the y-coordinate of the vertex can be found by substituting the x-coordinate into the original quadratic equation.
Watch the video below to hear more about how to determine the key features of a parabola from its equation, as well as see some examples of different parabolas and their key features.
Watch the video below to see some examples of how to graph quadratic equations by hand through first identifying the key features including the intercepts, the vertex, and the axis of symmetry.
Complete the worksheet attachment below and then check your answers using the solutions attachment. Once you have completed these exercises, click the link to advance to the course home page.