Teaching Notes 5.22: Solving Quadratic Equations Using
the Quadratic Formula
The quadratic formula can be used to solve quadratic equations. Students often have trouble
using this formula because of the three variables, square roots, and fractions.- Explain that the quadratic formula can be used to solve quadratic equations. But before it can
be used the equation must be written in standard form.ax^2 +bx+c=0wherea=0. - Review the information and example on the worksheet with your students. Be sure that they
understand both the quadratic formula and the standard form of a quadratic equation. Note
that the equation in the example is already written in standard form. (If necessary, review
how to express an equation in standard form by adding the same term to or subtracting the
same term from both sides of the equation.) Point out that the expression inside the radical
symbol must be greater than or equal to 0 because the square root of a negative number is
not a real number. Discuss the steps for using the quadratic formula to solve an equation.
Depending on the abilities of your students, you may find it necessary to demonstrate the
order of operations.
EXTRA HELP:
Use the order of operations to solve forx.Simplify the expression inside the radical symbol, find
the square root, simplify the numerator, and then divide.ANSWER KEY:
(1)x=2andx= 3 (2)x=4andx=− 1 (3)x=−3andx− 6 (4)x=− 5
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(Challenge)You would first need to rewrite the equation in the standard form by addingxto
both sides of the equation and subtracting 12 from both sides of the equation. Then you could
solve the equation using the quadratic formula, substituting 1 fora,1forb,and−12 forc.The
correct solutions arex=−4andx=3.
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