Graphs of Quadratic Equations2/19/2013

Warm-Up

Homework Check

Review Practice: Simplify: 1.

2.

3.

4.

Review1. 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

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 Solutions 1 Solution 2 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:

x

y

Ex 2:

1. Standard Form:______________2. Graph: 3. Vertex: ____4. Axis of symmetry: _____5. y-intercept:_____6. x-intercept:_____7. Solutions:

x

y

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:

x

y

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=-16t2 + 30.  

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 = -16t2 + 26 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 = x2 – 25x + 5000. Find the minimum profit.