Elementary algebra

Section 4-6: The Quadratic Formula and the Discriminant The standard form of a quadratic is: +('' The quadratic formula is: )(. - - , where a, b, and c are real numbers where a # 0. - > What is the purpose of using the quadratic formula? : / What is the expression used to find the discriminant: \ > What information does the discriminant tell you? / (IC IS Value of Discriminant: ( Number and types of 'I \ ( solutions: Graph will look like: Find the discriminant of the quadratic equation and give the number and type of solutions of the equation. Ex 1) a. x2 +6x+11 b.x2 +6x+9 c.x2 +6x+5 1 - - L - Identify the discrimant of-eacb of-the following equations and state how many solutions and what

Section 4.5: Vertex form with Completing the Square Completing the Square: Used to change quadratic functions in standard form to vertex form. f (x) = ax 2 + bx + c - f(x)=a(x?h) 2 +k ------------------------ Investigation This creates a Perfect Square 2 (b)2 Tririomiai, which factors To complete the square for an expression x + bx, add ------ Startwithx2 + bx Find (b)2 x2 +bx+() (x+ )2 / The Completed Square Factored form x2 +6x - x2 +4x 2 X - 8x _) - X - 2x oF W4CX 1rrrt! You Try?Complete the Square for the following. Then write the factored form. 1)x2 +14x 2)y2 +20y 2t\2S io) IOD (xiiJJ _ 0) 3)m2 -IOM L Omtn - 15 ) ;4 6 7 4)h2 -15h '4 P7 L_'1-' & ? **How do we go from standard form of mAquation to vertex form?

?6= ?2 b) 25 c) 7(x-4)2 ?18=10 tt fS )c 100 - f(TI1)jii Solving Quadratic Equations by Finding Square Roots Objective: To solve quadratic equations with real solutions. If R2=S, then Risa (00+ of S. A positive number S has 2 square roots written as ( and . ?O Properties: Product Property: V'-a- Quotient Property:Tb Simplify the expression (radical) a) b) c) id * 1-5 Rationalize Denominators of fractions 1 1 5D re: a, / 1,0 a) J ~S? I- b) 2 rOL - I Steps to solving quadratic equations: Step 1: Write the original equation - V+3f 1:-- ?4 } d) I? '- V64 '4L.f Form of the denominator Multiply numerator and denominator by: (multiply the _by_ _conjugate) puC 3 - j --3)-2 i_i0 (7+) ?- F (p

Name: Date: Section 4-2 Notes Graphing Quadratic Functions in ird For Standard form of a quadratic function is E ax - A The parent function of the family of all quadratic functions is f(x) The graph of a quadratic function is a DaYWO01 IA. The vertex of a parabola is the or point on the parabola. .-.J 00 The axis of jcnY1LeA-rJ7 divides the parabola into mirror images and passes through the Graph the function y = CoWare to Graph the function y = (_--x)2. Compare it to -1 '/q 00 Thej X~'M The graph of a parabola is more vertically stretched than the parent function if 1 1k 1 > I The graph of a parabola is more vertically compressed than the parent function if The graph of a parabola is more horizontally stretched than the parent function if" I