Vertex; (-2,-4); passes through (-1, -6) Do Now 3/27/19 Take out HW from last night. Text p. 446, #20-44 evens Copy HW in your planner. Text p. 446, #6-12 evens, #58-62 evens Puzzle Time 8.4 In your notebook, write a quadratic function in vertex form and standard form whose graph has the given vertex and passes through the given point. Vertex; (-2,-4); passes through (-1, -6)

Vertex; (-2,-4); passes through (-1, -6) On Your Own Write a quadratic function in vertex form whose graph has the given vertex and passes through the given point. Vertex; (-2,-4); passes through (-1, -6) y = -2(x + 2)2 –4 y = -2x2 - 8x - 12

Homework Text p. 446, #20-44 evens

Homework Text p. 446, #20-44 evens

Homework Text p. 446, #20-44 evens

Homework Text p. 446, #20-44 evens

Learning Goal Learning Target SWBAT graph quadratic functions SWBAT practice graphing functions of the form f(x) = a(x – h)² + k

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.

The Graph of f(x) = a(x – h)² When h > 0, the graph of ax2 is translated RIGHT h units. When h < 0, the graph of ax2 is translated LEFT h units.

The Graph of f(x) = a(x – h)² + k When k > 0, the graph of ax2 is translated UP k units. When k < 0, the graph of ax2 is translated DOWN k units.

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

Graph the Following Functions. Compare to the graph of f(x) = x2. On Your Own Graph the Following Functions. Compare to the graph of f(x) = x2. h(x) = 1/2(x + 4)2 - 2 h(x) = -(x – 2)2 The graph of h is a vertical shrink by a factor of 1/2, and a translation 3 units left and 2 units down of the graph of f. The graph of h is a horizontal translation 2 units right and a reflection in the x-axis of the graph of f.

Vertex; (-5, 6); passes through (-3, 8) Write a quadratic function in vertex form AND standard form whose graph has the given vertex and passes through the given point. Vertex; (-5, 6); passes through (-3, 8) y = a(x - h)2 + k y = a(x + 5)2 + 6 8 = a(-3 + 5)2 + 6 8 = a(2)2 + 6 8 = 4a + 6 y = 1/2(x + 5)2 + 6 2 = 4a 1/2 = a y = 1/2x2 + 5x + 37/2

Identifying EVEN or ODD functions A function y = f(x) is... when f(-x) = -f(x) when f(-x) = f(x) The graph is symmetric about the origin after reflections in the x-axis and then the y-axis. The graph is symmetric about the y-axis. EVEN means SAME ODD means OPPOSITE NEITHER means DIFFERENT (besides opposite) Khan Academy video tutorial

EVEN ODD Identifying EVEN or ODD functions Is the function EVEN, ODD, or NEITHER? EVEN ODD When f(-x) = f(x) When f(-x) = -f(x) f(x) = 2x f(x) = x2-2 f(-x) = 2(-x) f(-x) = (-x)2-2 Substitute -x Substitute -x f(-x) = -2x Simplify f(-x) = x2-2 Simplify f(-x) = -2x f(x) = 2x f(-x) = x2-2 f(x) = x2-2 Compare Compare OPPOSITE means ODD SAME means EVEN

Is the function EVEN, ODD, or NEITHER? TRY IT OUT… Is the function EVEN, ODD, or NEITHER? f(x) = 4x2 f(x) = x2-2x+3 Substitute -x f(-x) = 4(-x)2 f(-x) = (-x)2-2(-x)+3 Substitute -x f(-x) = 4x2 Simplify f(-x) = x2+2x+3 Simplify f(-x) = 4x2 f(x) = 4x2 f(-x) = x2-2x+3 f(x) = x2+2x+3 Compare Compare SAME means EVEN DIFFERENT means NEITHER

With your 2:00 partner, complete PuzzleTime worksheet 8.4 - Schoology Guided Practice With your 2:00 partner, complete PuzzleTime worksheet 8.4 - Schoology

Homework Puzzle Time worksheet 8.4 Text p. 446, #6-12 evens, #58-62 evens