1. Determine if each is a quadratic equation or not.
Warm – Up 2.8
Determine if each is a quadratic equation or not.
y = 8x2 – 3x + 5
y = 9 – 10x + 3x2 – 6x4
y = -5x2
y = 3x – 2

2. Algebra 3
Lesson 2.8
Objective: SSBAT find the vertex of a quadratic function and graph the quadratic function.
Standards: M11.D.2.1.2

3. Graph of a Quadratic Equation
Called a PARABOLA
U – Shaped
 The Graph will open UP if the x2 term is Positive.
 The Graph will open DOWN if the x2 term is Negative.

4. Determine if the parabola (graph) for each will open upwards or downwards. Tell why.
y = 12x2 – 3x – 9
y = -x2 – 5x
y = 18 – 2x2
y = 9 – 12x + 4x2
 Up because 12x2 is positive
 Down because -x2 is negative
 Down because -2x2 is negative
 Up because 4x2 is positive

5.  The point at which the parabola reaches a maximum or minimum.
Vertex
 The point at which the parabola reaches a maximum or minimum.
The vertex is a Minimum
The vertex is a Maximum
 The y-value of the vertex point is the Maximum or Minimum value of the function

6. Axis of Symmetry
The vertical line that divides a parabola into 2 parts that are mirror images
It is always a vertical line that goes through the vertex
The equation is: x = x-coordinate of vertex

7. Identify the vertex of each. State if it is a Max or Min.1.
Vertex: (-2, 6)
Maximum

8. 2.
Vertex: (1, -1)
Minimum

9. Corresponding Points
Each point of the parabola has a corresponding point on its mirror image
Two corresponding points are the same distance from the axis of symmetry
 Corresponding point to point P is (5, 6)
 Corresponding point to point Q is (2, 3)

10. Find the corresponding point to each point given below.

11. Finding the vertex of a quadratic equation.
Make sure the equation is in standard form. y = ax2 + bx + c
1. Find the x-coordinate by using the formula
x =
2. Find the y-coordinate by substituting the x-value from above into the beginning equation and solve for y

12. *Continue on next slide *
Find the vertex of each quadratic function.
y = -3x2 – 12x + 10
a = b = c = 10
x =
= -2
x = -2
*Continue on next slide *

13. Continued. y = -3x2 – 12x + 10
Find y by putting -2 in for x into the original function
y = -3(-2)2 – 12(-2) + 10
y = 22
Vertex: (-2, 22)

14. *Continue on next slide *
Teacher
y = -x2 + 2x + 1
a = b = 2 c = 1
x =
= 1
x = 1
*Continue on next slide *

15. 2. Continued. y = -x2 + 2x + 1
Find y by putting 1 in for x into the original function
y = -(1)2 + 2(1) + 1
y = 2
Vertex: (1, 2)

16. 3.
a = b = 2 c = -1
x =
x = -3
Continue on next slide

17. 3. Continued.
Find y by putting -3 in for x into the original function
y = -4
Vertex: (-3 , -4)

18. 4. y = 5x2 + 11 x = x = 0 y = 5(0)2 + 11 y = 11 Vertex: (0, 11)
a = 5 b = 0 c = 11
x =
x = 0
y = 5(0)2 + 11
y = 11
Vertex: (0, 11)

19. 1. 2. Vertex: (3, -1) Vertex: (3, -8.5)
Teacher
On Your Own: Find the Vertex of each.
Vertex: (3, -1)
Vertex: (3, -8.5)

20. Homework
Worksheet 2.8