1. SAT Problem of the Day

2. SAT Problem of the Day

3. SAT Problem of the Day

4. SAT Problem of the Day

5. 5.4 Completing the Square Objectives:
Use completing the square to solve a quadratic equation
Use the vertex form of a quadratic function to locate the axis of symmetry of its graph

6. Example 1
Complete the square for each quadratic expression to form a perfect-square trinomial.
find
a) x2 – 10x
x2 – 10x + 25
(x - 5)2
find
b) x2 + 27x

7. Practice
Complete the square for each quadratic expression to form a perfect-square trinomial. Then write the new expression as a binomial squared.
1) x2 – 7x
2) x2 + 16x

8. Example 2 Solve x2 + 18x – 40 = 0 by completing the square. find
x = 2 or x = -20

9. Practice Solve by completing the square. 1) x2 + 10x – 24 = 0

10. Example 3 Solve x2 + 9x – 22 = 0 by completing the square. find
x + 9/2 = +13/2 or -13/2
x = 2 or x = -11

11. Practice
Solve by completing the square.
1) x2 - 7x = 14

12. Example 4 Solve 3x2 - 6x = 5 by completing the square. find

13. Vertex Form
If the coordinates of the vertex of the graph of y = ax2 + bx + c, where are (h,k), then you can represent the parabola as y = a(x – h)2 + k, which is the vertex form of a quadratic function.

14. Example 5
Write the quadratic equation in vertex form. Give the coordinates of the vertex and the equation of the axis of symmetry.
vertex form:
y = a(x – h)2 + k
y = -6x2 + 72x - 207
y = -6(x2 - 12x) - 207
y = -6(x2 - 12x
+ 36)
– 207 +
216
y = -6(x - 6)2 + 9
vertex: (6,9)
axis of symmetry: x = 6

15. Example 6
Given g(x) = 2x2 + 16x + 23, write the function in vertex form, and give the coordinates of the vertex and the equation of the axis of symmetry. Then describe the transformations from f(x) = x2 to g.
g(x) = 2x2 + 16x + 23
vertex form:
y = a(x – h)2 + k
= 2(x2 + 8x) + 23
= 2(x2 + 8x
+ 16)
+ 23
– 32
= 2(x + 4)2 - 9
= 2(x – (- 4))2 + (-9)
vertex: (-4,-9)
axis of symmetry: x = -4

16. Application
A softball is thrown upward with an initial velocity of 32 feet per second from 5 feet above ground. The ball’s height in feet above the ground is modeled by
h(t) = -16t2 + 32t + 5, where t is the time in seconds after the ball is released. Complete the square and rewrite h in vertex form. Then find the maximum height of the ball.
Objectives:
Use the vertex form of a quadratic function to locate the vertex, the axis of symmetry, and describe the graph.

17. Collins Type II
As an exit ticket, explain what exactly h and k represent (vertex form) for the application problem.
Use specific terms from the problem
Objectives:
Use the vertex form of a quadratic function to locate the vertex, the axis of symmetry, and describe the graph.

18. Practice
Given g(x) = 3x2 – 9x - 2, write the function in vertex form, and give the coordinates of the vertex and the equation of the axis of symmetry. Then describe the transformations from f(x) = x2 to g.
Objectives:
Use the vertex form of a quadratic function to locate the vertex, the axis of symmetry, and describe the graph.

19. Homework
Lesson 5.4 exercises ODD