1. 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)

2. 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

3. Homework Text p. 446, #20-44 evens

4. Homework Text p. 446, #20-44 evens

5. Homework Text p. 446, #20-44 evens

6. Homework Text p. 446, #20-44 evens

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

8. 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.

9. 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.

10. 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.

11. 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)

12. 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

13. 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.

14. 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

15. 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

16. 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

17. 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

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

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