Answer:
Real World Examples of
Quadratic Equations
Quadratic Equation
Quadratic equations pop up in many real world situations!
Here we have collected some examples for you, and solve each using different methods:
Factoring Quadratics
Completing the Square
Graphing Quadratic Equations
The Quadratic Formula
Online Quadratic Equation Solver
Each example follows three general stages:
Take the real world description and make some equations
Solve!
Use your common sense to interpret the results
Example: Small Steel Frame
area=28
Your company is going to make frames as part of a new product they are launching.
The frame will be cut out of a piece of steel, and to keep the weight down, the final area should be 28 cm2
The inside of the frame has to be 11 cm by 6 cm
What should the width x of the metal be?
Area of steel before cutting:
Area = (11 + 2x) × (6 + 2x) cm2
Area = 66 + 22x + 12x + 4x2
Area = 4x2 + 34x + 66
Area of steel after cutting out the 11 × 6 middle:
Area = 4x2 + 34x + 66 − 66
Area = 4x2 + 34x
quadratic 4x^2 + 34x
Let us solve this one graphically!
Here is the graph of 4x2 + 34x :
The desired area of 28 is shown as a horizontal line.
The area equals 28 cm2 when:
x is about −9.3 or 0.8
The negative value of x make no sense, so the answer is:
x = 0.8 cm (approx.)
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