We begin by recalling that a quadratic equation can have zero, one, or two solutions.
ax^2+bx+c = 0
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Zero One Two
If there are two solutions, we need to consider the context of the real-world situation to determine whether one or both solutions answer the given question.
Extra
Examples of Real-World Situations
Let's see some examples of real-world situations that use quadratic equations.
Example 1
Let h(t)=- t^2+3t+10 be a function that gives the height of a ball t seconds after being thrown from a height of 10 meters above the ground. To find the time at which this ball hits the ground, we must equate the function to 0.
h(t) = - t^2+3t+10 = 0
Next, let's solve the equation above for t.
As we can see, we have found two solutions, t=-2 and t=5. However, since t represents time, it cannot be negative and we discard t=-2. In consequence, we conclude that the ball will hit the ground 5 seconds after being thrown.
Example 2
The function R(p)=- p^2+10p+479 gives the revenue of a company when they set the price of their product as p dollars. Let's find the price per product for which the company makes a profit of $500.
R(p)=- p^2+10p+479 = 500
Let's solve the equation above by factoring.
