Graphs of Quadratic Equations 2/19/2013. Warm-Up.

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Presentation transcript:

Graphs of Quadratic Equations 2/19/2013

Warm-Up

Homework Check

Review Practice: Simplify:

Review 1.Find the perimeter Of the rectangle: 2. If the perimeter of the trapezoid is 13x – 9. Find the missing side length: 3x - 8 6x + 4 2x + 8 5x + 13 ?

Answer the Questions:

The two functions we have just looked at are called quadratic functions. **The graph of a quadratic function is a U-shaped curve called a parabola.

Complete the investigation: Pairs will display their work under the doc cam. Make sure your work is neat!!!

There are 3 possible choices for solutions for quadratic equations: Solutions are your x-intercepts!!! 0 Solutions1 Solution2 Solutions The domain is always ____________ for quadratic functions. All real numbers

Use a graphing calculator to answer the following questions. All equations must be in y= before we can graph them using the calculator. Ex. 1 1.Standard Form:__________ 2.Graph: 3.Vertex: ____ 4.Axis of symmetry: _____ 5.y-intercept:_____ 6.x-intercept:_____ 7.Solutions:

Ex 2: 1.Standard Form:______________ 2.Graph: 3.Vertex: ____ 4.Axis of symmetry: _____ 5.y-intercept:_____ 6.x-intercept:_____ 7.Solutions:

Ex 3: 1.Vertex: ____ 2.Axis of symmetry: _____ 3.y-intercept:_____ 4.x-intercept:_____ 5.Solutions:

Ex 4: 1.Standard Form:______________ 2.Graph: 3.Vertex: ____ 4.Axis of symmetry: _____ 5.y-intercept:_____ 6.x-intercept:_____ 7.Solutions:

1. Suppose an eagle is flying 30 feet above a canyon when it drops a stick from its claws. The height, h, of the stick t seconds after it is released can be modeled by the function h=-16t A.How high above the ground is the stick after 1 second? B. When will the stick hit the ground? (The height when an object hits the ground is 0.)

1C Look at the graph. Why is only the first quadrant shown?

2. A monkey drops an orange from a branch26 ft above the ground. The force of gravity calls the orange to fall to earth. The function h = -16t gives the height of the orange h in feet after t seconds. When will the orange hit the ground? (The height when an object hits the ground is 0.)

3. Use a graph to answer the following questions. Use a graph to find the minimum/maximum points (vertex)! A. The total profit made by an engineering firm is given by the function p = x 2 – 25x Find the minimum profit.