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Graphs of Quadratic Equations2/19/2013
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Warm-Up
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Homework Check
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Review Practice: Simplify: 1.
2.
3.
4.
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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
?
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Answer the Questions:
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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.
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Complete the investigation:
Pairs will display their work under the doc cam.
Make sure your work is neat!!!
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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
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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
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Ex 2:
1. Standard Form:______________2. Graph: 3. Vertex: ____4. Axis of symmetry: _____5. y-intercept:_____6. x-intercept:_____7. Solutions:
x
y
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Ex 3:1. Vertex: ____2. Axis of symmetry: _____3. y-intercept:_____4. x-intercept:_____5. Solutions:
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Ex 4:
1. Standard Form:______________2. Graph: 3. Vertex: ____4. Axis of symmetry: _____5. y-intercept:_____6. x-intercept:_____7. Solutions:
x
y
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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.)
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1C
Look at the graph. Why is only the first quadrant shown?
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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.)
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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.