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

. Teacher (Magnani) 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

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.

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

 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

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

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

2. Vertex: (1, -1) Minimum

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)

Find the corresponding point to each point given below.

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

*Continue on next slide * Find the vertex of each quadratic function. 1. y = -3x2 – 12x + 10 a = -3 b = -12 c = 10 x = = -2 x = -2 *Continue on next slide *

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)

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

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)

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

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

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)

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

Homework Worksheet 2.8