Lesson 2: 3-2 Solving Quadratic Equations by Graphing

1. What is the difference between a quadratic function and a quadratic equation?
2. What is the purpose of setting the quadratic function equal to zero?
3. What is the graphic meaning of the zeros of a quadratic equation?
4. In what two cases could a quadratic equation have no zeros?
5. In what case could a quadratic equation have one zero?

Quadratic Equation
Standard Form
Root
Zero

A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

SAT questions related to solving quadratics: 2-3-13,3-3-14,1-3-16,5-3-3,8-3-16,1-4-25; analyzing graphs: 3-4-12,8-3-11,8-4-19,6-3-11

If the graph of the related quadratic function has one x-intercept, then there is one real solution (double root). If the graph of the related quadratic function has two x-intercepts, then there are two real solutions. If the graph of the related quadratic function does not intersect the x-axis, then there are no real solutions, but two imaginary solutions.

Arielle works in the marketing department of a major retailer. Her job is to set prices for new products sold in the stores. Arielle determined that for a certain product, the function f(p)=-6p^2+192p-1440 tells the profit f(p) made at price p. Arielle can determine the price range by finding the prices for which the profit is equal to $0. This can be done by finding the solutions of the related quadratic equation 0=-6p^2+192p-1440. The graph of the function indicates that the profit is zero at 12 and 20, so the profitable price range of the item is between $12 and $20.

You will see in later chapters that many zeros can appear within small intervals.

Provide students with a variety of parabolas. Ask students to sort the parabolas into three piles: those that model a quadratic equation with one real solution, those that model a quadratic equation with two real solutions, and those that model a quadratic equation with no real solutions. Finally, ask students to name the real solutions for those in the piles having real solutions.

McGraw Hill resources

McGraw Hill resources