Download 7.3 The Discriminant Vocabulary D = b2 - 4ac

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7.3 The Discriminant
Tuesday, July 17, 2012
Vocabulary
• Discriminant: the part of the quadratic formula under the radical, often denoted
by D
D = b2 - 4ac
It allows us to determine the nature of the roots of a quadratic
Remember, the roots of a quadratic are calculated as follows:
Calculate the discriminant, then calculate the roots:
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The Nature of the Roots of a Quadratic Equation:
Let ax2 + bx + c = 0 be a quadratic equation with real coefficients
1. If b2 - 4ac > 0, there are 2 unequal roots
2. If b2 - 4ac = 0, there is one real double root
3. If b2 - 4ac < 0, there are 2 conjugate imaginary roots
Test for Rational Roots
If a quadratic has integral coefficients and its discriminant is a perfect square,
then the equation has rational roots.
If a quadratic equation can be transformed into an equivalent equation that meets
this test, then it has rational roots
Methods for Solving Quadratic Equations:
1. Factoring if the discriminant is a perfect square
2. Completing the Square if the equation has the form: x2 + (even number)x +
constant = 0
3. Quadratic Formula always works, but may be more time consuming
4. Graphing if the discriminant is > 0. Will not work with imaginary roots
Word Problems:
The volume of a rectangular jewelry box 4cm in height is 136 cm3. If the
perimeter of the base is 24 cm, find the dimensions of the base.
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A 5 in. by 7 in. photograph is surrounded by a frame of uniform width. The area of
the frame equals the area of the photograph. Find the width of the frame.
A box with a square base and no lid is to be made from a square piece of metal by
cutting squares from the corners and folding up the sides. The cut-off squares are
5 cm on a side. If the volume of the box is 100 cm3, find the dimensions of the
original piece of metal.
Equations in Quadratic Form
Tuesday, July 17, 2012
10:28 PM
7-4 Equations in Quadratic Form
Vocabulary
• Quadratic Form: any equation that can be written:
Where a is not equal to 0 and f(x) is some function of x.
To solve: replace f(x) with a single variable.
Examples:
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Practice:
Homework: MathXL 7.3-7.4 HW
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