Ch. 9.3 Vertex to General Form. of a Parabola

Transcription

1 Ch. 9.3 Verte to General Form Learning Intentions: of a Parabola Change a quadratic equation from verte to general form. Learn to square a binomial & factor perfectsquare epressions using rectangle diagrams. Solve problems using a quadratic equation that models projectile motion.

2 Recall: Identify & label the roots, verte & ais of symmetry of the given parabola. y

3 SOLUTION: Identify & label the roots, verte & ais of symmetry of the given parabola. y = h root (-intercept) (h, k) verte root (-intercept) ais of symmetry

4 Vocabulary

5 Polynomials are sums of these "variables and eponents" epressions. Each piece of the polynomial, each part that is being added, is called a "term". Polynomial terms have variables which are raised to whole-number eponents (or else the terms are just plain numbers); there are no square roots of variables, no fractional powers, and no variables in the denominator of any fractions. Here are some eamples: 6 This is NOT a polynomial term......because the variable has a negative eponent. Eample of a typical polynomial: 1 / sqrt() 4 This is NOT a polynomial term... This is NOT a polynomial term... This IS a polynomial term......because the variable is in the denominator....because the variable is not to an integer power ^(1/)....because it obeys all the rules. Notice the eponents on the terms. The first term has an eponent of ; the second term has an "understood" eponent of 1; and the last term doesn't have any variable at all. Polynomials are usually written this way, with the terms written in "decreasing" order; that is, with the largest eponent first, the net highest net, and so forth, until you get down to the plain old number. Any term that doesn't have a variable in it is called a "constant" term because, no matter what value you may put in for the variable, that constant term will never change. In the picture above, no matter what might be, 7 will always be just 7. The first term in the polynomial, when it is written in decreasing order, is also the term with the biggest eponent, and is called the "leading term". The eponent on a term tells you the "degree" of the term. For instance, the leading term in the above polynomial is a "second-degree term" or "a term of degree two". The second term is a "first degree" term. The degree of the leading term tells you the degree of the whole polynomial; the polynomial above is a "second-degree polynomial". Here are a couple more eamples:

6 Vocabulary degree: of a polynomial or function is the power of the term that has the greatest eponent. general form: of a polynomial is when the degrees of the terms decrease from left to right. monomial: a polynomial that has only one term. Polynomial eponents must be non-negative integers binomial: a polynomial with two terms. trinomial: a polynomial with three terms. polynomial : more than three terms OR unspecified number of terms (could be any of the above).

7 Identify the degree of each polynomial.

8 Solutions: Identify the degree of each polynomial.

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11 Copy each rectangle diagram and fill in the missing values. Then write a squared binomial & an equivalent trinomial that both represent the total area of each diagram

12 Solutions: Copy each rectangle diagram and fill in the missing values. Then write a squared binomial & an equivalent trinomial that both represent the total area of each diagram. A = ( + ) = A = ( 7) = A = ( + 1) = ( + 1)( + 1)= F O I L

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15 Draw a rectangle diagram for each epression. Verify that the area is equivalent to the algebraic simplification of each given. ( 5) ( 11) ( 3) ( 13)

16 Solutions: Draw a rectangle diagram for each epression. ( 5) ( 11) = ( + 11)( + 11) = = ( 3) ( 13)

17 From Verte Form To General Form Verte form y a( h ) k General form y a b c How do we convert the verte form equation to general form?

18 From Verte Form To General Form y y a( h) k a b c

19 Convert each equation from verte form to general form. y ( 5) 4 y 3( 4) 1

20 Solution: Convert each equation from verte form to general form. y ( 5) 4 y 3( 4) 1 9

21 Writing a Verte Form Equation Given: General Form / parabola E.) Consider the graph of the parabola y 4 7

22 SOLUTION: E.) Writing Verte Form Equations Consider the graph of the parabola y 4 7

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