2ParabolaThe graph of any quadraticfunction.It is a kind ofcurve.
3Where are parabolas seen in the real world? The Arctic PoppySatellite DishesThe Golden Gate BridgeTrajectoryHeadlights
4Why is the parabola important? Suspension Bridges use a parabolic design to evenly distribute the weight of the entire bridge to the supporting columns.
5Why is the parabola important? The Satellite Dish uses a parabolic shape to ensure that no matter where on the dish surface the satellite signal strikes, it is always reflected to the receiver.
6Why is the parabola important? A car’s Headlights, and common flashlights, use parabolic mirrors to project the light from the bulb into a tight beam, directing the light straight out from the car, or flashlight.
18Check It Out! Example 2bGraph the quadratic function.y = –3x2 + 1Make a table of values.Choose values of x anduse them to find valuesof y.x–2–112y1–2–11Graph the points. Then connect the points with a smooth curve.
21Check It Out! Example 2aGraph each quadratic function.y = x2 + 2Make a table of values.Choose values of x anduse them to find valuesof y.x–2–112y236Graph the points. Then connect the points with a smooth curve.
22Additional Example 3A: Identifying the Direction of a Parabola Tell whether the graph of the quadratic function opens upward or downward. Explain.Write the function in the formy = ax2 + bx + c by solving for y.Addto both sides.Identify the value of a.Since a > 0, the parabola opens upward.
23Additional Example 3B: Identifying the Direction of a Parabola Tell whether the graph of the quadratic function opens upward or downward. Explain.y = 5x – 3x2Write the function in the form y = ax2 + bx + c.y = –3x2 + 5xa = –3Identify the value of a.Since a < 0, the parabola opens downward.
24Check It Out! Example 3aTell whether the graph of each quadratic function opens upward or downward. Explain.f(x) = –4x2 – x + 1f(x) = –4x2 – x + 1Identify the value of a.a = –4Since a < 0 the parabola opens downward.
25Lesson Quiz: Part I1. Without graphing, tell whether (3, 12) is on the graph of y = 2x2 – 5.2. Graph y = 1.5x2.no
26Lesson Quiz: Part IIUse the graph for Problems 3-5.3. Identify the vertex.4. Does the function have a minimum or maximum? What is it?5. Find the domain and range.(5, –4)maximum; –4D: all real numbers;R: y ≤ –4