Chapter Notes Alg. H -A (Lesson -) Solving Quadratic Equations b Finding the Square Root and Completing the Square p. *Calculator Find the Square Root: take the square root of. E: Solve b finding square roots. Round to the nearest tenth. ) m m 0 ) b b ) m m 0 Steps for Completing the Square:. If necessar, divide both sides b.. Isolate the terms.. Divide the coefficient of b ; it.. Add that number to of the equation.. the trinomial as or.. Take the of each side.. for. Notes Ch. Alg. H
Eamples: Solve b completing the square. Leave answers in radical form where necessar. ) ) 0 0 0 Solve b completing the square. Round answers to the nearest tenth where necessar. ) n n 0 ) Notes Ch. Alg. H
-A/ (Lesson Heath. and Glencoe -) Graphing Quadratic Functions (Verte Form) Heath p. - Standard Form: Completed Square Form (Verte Form): Parabola: Verte: o Minimum: o Maimum: Ais of smmetr: the line that divides a into halves o Equation: To sketch a parabola: ) Find the. Use the Completed Square/Verte to find the values of h and k Write the Verte as an ordered pair: ) Make a of values. Choose at least additional values of. values than the -value of the verte and values that are. to find values and complete the table.. ) Plot the and draw a. verte: (, ) 0-0 - - - - - - - - 0 - - - - - - - - -0 Notes Ch. Alg. H
. verte: (, ) 0-0 - - - - - - - - 0 - - - - - - - - -0. 0 verte: (, ) -0 - - - - - - - - 0 - - - - - - - - -0. Phsics Problem Eample: (Use graphing to solve) Miranda throws a set of kes up to her brother, who is standing on a balcon ft. above the ground. She throws with a velocit of 0 ft/sec. and her hand is ft. off the ground. How long does it take the kes to reach their highest point? Will her brother be able to catch the kes? Notes Ch. Alg. H
. -A (Lesson -) Solving Quadratic Equations b Graphing & Finding Roots Quadratic Equation: (standard form) Roots: Zeros: Check: b c c 0 verte: (, ) 0-0 - - - - - - - - 0 - - - - - - - - -0 p. 0. 0 verte: (, ) 0-0 - - - - - - - - 0 - - - - - - - - -0. t t verte: (, ) 0-0 - - - - - - - - 0 - - - - - - - - -0 Notes Ch. Alg. H
Use Factoring first to determine how man times the graph the. f 0. 0 Factor: -0 - - - - - - - - 0 - - - - - - - - Intersections: Roots: Integral Roots: If roots aren t integers, ; write solution as a compound. a a 0-0 0-0 - - - - - - - - 0 - - - - - - - - -0 Notes Ch. Alg. H
-A Notes Quadratic Word Problems *calculator Alg. H EX : The path of a ball kicked against a wall (the ais is the wall) follows the path = + +, where is the height of the ball in feet, and is the horizontal distance (in feet) from the wall. A) How high is the ball at its maimum height? B) How far above the ground does the ball hit the wall? (The ais represents the wall.) EX : In the diagram below, the backboard is located on the -ais and the hoop is located at the point (,0). A basketball thrown toward the hoop follows the path =. +. +. where and are measured in feet. A) When the ball was at its highest point, what was its horizontal distance from the backboard? (Round to two decimal places.) B) At its highest point, how far off the ground was the basketball? EX : How deep is the pond given b the equation = +? Pthagorean Theorem: Notes Ch. Alg. H
-A (Lesson -A) Solving Quadratic Equations b Using the Quadratic Formula CALCULATOR p. - Quadratic Formula: Used to solve Quadratic Equations: b b ac a Read E. A... a = b = c = B. a = b = c = C.) A roofer tosses a piece of roofing tile from a roof onto the ground 0 ft below. He tosses the tile with an initial velocit of 0 ft. per second. How long does it take the tile to hit the ground? h t vt s Notes Ch. Alg. H
-A (Lesson -B) Using the Discriminant p. - Discriminant: the (epression inside the radical smbol); part of the formula b b ac a Three possibilities for the discriminant: No Solution 0 One Solution Two Solutions (Does not intersect the -ais) (Verte is on the -ais) (Intersects -ais at two points) b ac 0 b ac 0 b ac 0 b ac b ac b ac Read E. p. A. n 0n 0 B. 0 C. 0 When the discriminant is a perfect square, the solutions will be numbers Notes Ch. Alg. H
-A Derivation of Quadratic Formula and Choosing a Method Solve the following b completing the square: a b c 0 This is called the Derivation of the Which method should ou choose to solve a b c 0? (in order of preference and efficienc!) Choice Method When to Use When b = 0 To solve Lesson When easil Visual model Best when and b is an number An quadratic equation; gives solutions An quadratic equation; gives solutions Notes Ch. Alg. H 0
-A Eponential Functions p. 0-0 Standard Form: The variable is:. Graph: and 0-0 - - - - - - - - 0 - - - - - - - - -0. Graph: 0-0 - - - - - - - - 0 - - - - - - - - -0. Graph: 0-0 - - - - - - - - 0 - - - - - - - - -0 Notes Ch. Alg. H
. Graph: 0-0 - - - - - - - - 0 - - - - - - - - -0 Transforming a Graph of an Eponential Function: Change in Function Tpe of Change Positive or Negative Change in Graph b a Is it necessar to make a table when ou alread know the transformation? Notes Ch. Alg. H