Math Quadratics Notes and HW SolutionKey

Advanced Math Notes: Graphing and Evaluating in Quadratics [Day 2] Name: Key Quadratic Function in VERTEX FORM: y = a(x-h)² + k The graph opens: a > 0: UP a < 0: DOWN The graph looks like: a > 0: U a < 0: ∩ The vertex is a: a > 0: minimum value a < 0: maximum value How to find the vertex of the quadratic in VERTEX FORM: x coordinate "h": opposite of what's inside y coordinate "k": exactly what's outside Axis of symmetry: x = h How to graph a quadratic in VERTEX FORM: 1) put vertex in center of table 2) build table around vertex (pick 2 x's below and above "h") Example 1: Graph the given quadratic by finding the vertex and building a table around it. Identify the axis of symmetry, maximum or minimum value, domain and range (both in interval notation). f(x) = -(x-1)² + 2 a < 0: DOWN x | y ---|--- -1 | -2 0 | 1 1 | 2 (vertex) 2 | 1 3 | -2 axis of symmetry: x = 1 max or min: 2 domain: (-∞, ∞) range: (-∞, 2] Example 2: Graph the given quadratic by finding the vertex and building a table around it. Identify the axis of symmetry, maximum or minimum value, domain and range (both in interval notation). f(x)   = 2(x-3)² - 1 a > 0: UP x | y ---|--- -5 | 7 -4 | 1 -3 | -1 (vertex) -2 | 1 -1 | 7 axis of symmetry: x = 3 max or min: -1 domain: (-∞, ∞) range: [-1, ∞) Example 3: Graph the given quadratic by finding the vertex and building a table around it. Identify the axis of symmetry, maximum or minimum value, domain and range (both in interval notation). f(x)   = 1/2(x-3)² - 1 a > 0: UP x | y ---|--- 1 | -1/2 2 | -1 3 | -1 (vertex) 4 | -1/2 5 | 1 axis of symmetry: x = 3 max or min: -1 domain: (-∞, ∞) range: [-1, ∞) Advanced Math Quadratics [Day 2] HW: Graphing and Evaluating in Vertex Form Find the VERTEX of the quadratic equation that is given in vertex form. Also, state the value of a and tell whether the graph opens up or down.   1. y = 3(x+7)² + 4 vertex: (-7, 4) a = 3, opens: up 2. y = -1/2(x-5)² + 10 vertex: (5, 10) a = -1/2, opens: down Find the VERTEX of the quadratic equation that is given in vertex form. Also, state the value of a and tell whether the graph opens up or down.   3. y = 4(x - 1/2)² + 9 vertex: (1/2, 9) a = 4, opens: up 4. y = -(x + 6)² - 2 vertex: (-6, -2) a = -1, opens: down Graph the given quadratic by finding the vertex and building a table around it. Identify the axis of symmetry, maximum or minimum value, domain and range (both in interval notation).   5. y = (x + 4)² - 2 | x | y | |---|---| |-6 | 2 | |-5 | -1 | |-4 | -2 | (vertex) |-3 | -1 | |-2 | 2 | vertex: (-4, -2) axis of symmetry: x = -4 max or min: -2 domain: (-∞, ∞) range: [-2, ∞) 6. y = -(x - 3)² + 4 | x | y | |---|---| | 1 | 0 | | 2 | 3 | | 3 | 4 | (vertex) | 4 | 3 | | 5 | 0 | vertex: (3, 4) axis of symmetry: x = 3 max or min: 4 domain: (-∞, ∞) range: (-∞, 4]