Linear and Quadratic Functions: Solving Quadratic Functions

Solving Quadratic Equations Using the Quadratic Formula (continued)

Teacher writing on chalkboardLet’s go through one more example using the Quadratic Formula.

Solve n2 + 2n + 93 = 0 using the Quadratic Formula.

a = 1, b = 2 and c = 93

n equals negative two plus or minus the square root of the quantity two squared minus four times one times ninety three all over two times one

n is equal to negative two plus or minus the square root of the quantity four minus three hundred seventy two all over two

n is equal to negative two plus or minus square root of negative three hundred sixty eight all over two

n is equal to negative two plus or minus four i times square root of twenty three all over two

n is equal to negative one plus or minus two i times square root of twenty three

Real World Application: Solving Polynomial Equations

John is standing at the top of a building 4 units high.  He throws a ball off the roof and its path is defined by the function f(x) = -x2 + 4.  How many units from the base of the building does the ball hit the ground?

In this example, the best way to solve is to set the function equal to 0.  Why?  Well, when the ball hits the ground, the y-value is 0!

-x2 + 4 = 0
-x2 = -4
x2 = 4
x = -2, 2  (Note: -2 is excluded, since we cannot have a negative distance)

Therefore, the ball lands 2 units from the base of the building.

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