Do Now 4/3/19 Take out HW from last night. Copy HW in your planner. Text p. 465, #6-28 evens Copy HW in your planner. Text p. 447, #31, 35, 39, 43, 57 Text p. 455, #19, 23, 29, 49, 61 Text p. 465, #15, 17, 21, 23 Quiz sections 8.4-8.6 Thursday Search your computer or re-download the “How Are You Doing?” Chapter 8 Graphing Quadratic Functions worksheet from Schoology. Do Now 4/3/19

Homework Text p. 465, #6-28 evens

Homework Text p. 465, #6-28 evens

Learning Goal Learning Target SWBAT graph quadratic functions SWBAT review and practice graphing and writing quadratic functions in vertex form, intercept form and choosing functions to model data and write functions to model data

Section 8.4 “Graphing f(x) = a(x – h)² + k” Vertex Form of a quadratic function is the form f(x) = a(x – h)2 + k, where a ≠ 0. The vertex of the graph of the function is (h, k) and the axis of symmetry is h.

Find the axis of symmetry and vertex of the graph of the function f(x) = a(x – h)2 + k Vertex: (h, k) Axis of Symmetry: x = h y = -6(x + 4)2 - 3 y = -4(x + 3)2 + 1 Axis of Symmetry: Axis of Symmetry: x = -4 x = -3 Vertex: Vertex: (-4, -3) (-3, 1)

y = 3(x – 2)² – 1 Graph: y = a(x – h)² + k. Compare to f(x) = x2 1 2 “Parent Quadratic Function” y = x² Axis of x = h symmetry: x = 2 Vertex: (h, k) (2, -1) x y 1 2 11 x-axis The graph of y is a vertical stretch by a factor of 3, a horizontal translation right 2 units and a vertical translation down 1 unit. y-axis

Vertex; (1,2); passes through (3, 10) Write a quadratic function in vertex form whose graph has the given vertex and passes through the given point. Vertex; (1,2); passes through (3, 10) y = a(x - h)2 + k y = a(x - 1)2 + 2 10 = a(3 - 1)2 + 2 10 = a(2)2 + 2 10 = 4a + 2 8 = 4a y = 2(x - 1)2 + 2 2 = a

Section 8.5 “Using Intercept Form” of a quadratic function is the form f(x) = a(x – p)(x – q), where a ≠ 0. The x-intercepts are p and q and the axis of symmetry is .

Find the axis of symmetry, vertex, and zeros of the function f(x) = a(x – p)(x – q) Intercepts: p, q Axis of Symmetry: x = y = -(x + 1)(x – 5) y = (x + 6)(x – 4) Zeros: Zeros: x = -6 & 4 x = -1 & 5 Axis of Symmetry: Axis of Symmetry: x = -1 x = 2 Vertex: (2, 9) Vertex: (-1,-25)

y = -5x2 + 5x y = -5x(x - 1) x-axis y-axis Graph: y = a(x – p)(x – q). Describe the domain and range. y = -5x2 + 5x y = -5x2 + 5x Write in INTERCEPT form y = -5x(x - 1) Intercepts: x = 0; x = 1 Axis of x = symmetry: x = 1/2 Vertex: y = -5x(x + 1) x-axis y = -5(1/2)(1/2 + 1) (1/2, 5/4) The domain of the function is ALL REAL NUMBERS. The range of the function is y ≤ 5/4. y-axis

Zeros of a Function f(x) = -12x2 + 3 an x-value for which f(x) = 0. A zero of a function is an x-intercept of the graph of the function. f(x) = -12x2 + 3 Graph (Standard Form) Intercept Form (Factor) To find the zeros of a function, graph the function and locate the x-intercepts. f(x) = -12x2 + 3 f(x) = -3(4x2 – 1) f(x) = -3(2x – 1)(2x + 1) x = ½ and -½

Section 8.6 “Comparing Linear, Exponential, and Quadratic Functions” y = mx + b y = ax2+bx+c y = a(b)x

Comparing Linear, Exponential, and Quadratic Functions Differences and Ratios Linear Function the first differences are constant y = mx + b Exponential Function consecutive y-values are common ratios y = a(b)x Quadratic Function the second differences are constant y = ax2+bx+c

y = a(x – p)(x – q) y = a(x - 4)(x - 8) 12 = a(2 - 4)(2 - 8) Tell whether the table represents a linear, exponential, or quadratic function. Then write the function. The second differences are constant. Therefore, the function is quadratic. y = a(x – p)(x – q) y = a(x - 4)(x - 8) 12 = a(2 - 4)(2 - 8) y = 1(x - 4)(x - 8) 12 = a(-2)(-6) y = x2 -12x + 32 12 = 12a 1 = a

are constant. Therefore, the function is linear. Tell whether the table represents a linear, exponential, or quadratic function. Then write the function. The first differences are constant. Therefore, the function is linear. Common difference (slope) Y-value when x = 0.

Tell whether the table represents a linear, exponential, or quadratic function. Then write the function. Consecutive y-values have a common ratio. Therefore, the function is exponential. Y-value when x = 0. Commonratio.

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Homework Text p. 446, #31, 35, 39, 43, 57 Text p. 455, #19, 23, 29, 49, 61 Text p. 465, #15, 17, 21, 23 Quiz sections 8.4-8.6 Thursday