Graphing Quadratics With VERTEX and Axis of Symmetry At the end of the period, you will learn: 1. To...

Graphing QuadraticsWith VERTEX and Axis of Symmetry

At the end of the period, you will learn:

1. To compare parabola by the coefficient2. To find the vertex of a parabola

Warm-upGraph the quadratic equation by factoring.Tell whether the quadratic opens upward or

downward

1. y = - x2 + 7x + 12

2. f(x)= x2 + 21x + 20

3. y = - x2 - 6x + 8

Identifying Vertex

4

2

-2

-4

5

f(x) = 2x - x2

Vertex: (1,1)

Identifying Vertex Your turn! f(x) = x2 - 4

4

2

-2

-4

-5 5

Vertex: (0, -4)

Comparing Parabolay

x x - axis

y - axis

Green y = 5x2

Purple y = ½x2

Blue y = ¼ x2

Smaller coefficient = Wider parabola

Graphing with vertex

Vertex = (__, __)

4

2

-2

-4

-5 5

x y(__, __)0 –4

Formula in finding the vertex

x = –b_ 2a

y = substitute the value of x

y = ax2 + bx + c

Example

Find the vertex of y = -3x2 + 6x

+ 5

Formula in finding the vertex

x = –b_ 2a

y = substitute the value of x

x = –b_ 2a

x = –6 2(-3)

x = –6 –6

x = 1

y = substitute the value of x

y = -3x2 + 6x + 5

y = -3(1)2 + 6(1) + 5

y = -3 + 6 + 5

y = 8 Vertex = (1, 8)

Graph the Parabola

y = -3x2 + 6x + 5

Vertex = (1, 8)

y

x

2468

1 2 3 4 5

Your Turn!

Find the vertex of y = x2 + 2x –

5

Formula in finding the vertex

x = –b_ 2a

y = substitute the value of x

x = –b_ 2a

x = –2 2(1)

x = –22

x = –1

y = substitute the value of x

y = x2 + 2x – 5

y = 1 - 2 – 5

y = –6 Vertex = (-1, -6)

y = (–1)2 + 2(-1) – 5

Graph the Parabola

y

x

2468

1 2 3 4 5

y = x2 + 2x – 5Vertex = (-1, -

6)

Graphing QuadraticsReview on graphing quadratics

At the end of the period, you will master:

1. To graph parabola of this form: y = ax2

+ c

Classwork

Sketch the following parabola by finding the vertex

1. y = x2 + 4x + 3

5. y = - x2 + 4x - 4

2. y = –x2 + 4x – 4

6. y = –x2 + 8x – 5

4. y = x2 - 10x + 20

3. y = x2 + 3

Warm-up

Find the VERTEX and graph the PARABOLA

1. y = -3x2 + 6x + 5

Vertex = (1, 8)

2. y = x2 + 2x – 5Vertex = (-1, -

6)

3. y = x2 + 4x – 5

Vertex = (-2,-9)

4. y = x2 – 2

Vertex = (0, –2)

Formula in finding the vertex

x = –b_ 2a

y = substitute the value of x

y

x

Graphing: y = ax2 + c4. y = x2 – 2

Vertex = (0, –2)

5. y = x2 + 2

Vertex = (0, 2)y

x

Graphing: y = ax2 + c5. y = x2 + 2

Vertex = (0, 2)y

x

6. y = –x2 + 2

Vertex = (0, 2)y

x

ClassworkGraph the following parabola using:

I Finding the solution of the equations (Factoring)

II Finding the VERTEX (Using formula)

III Graphing on y-axis (using vertex)

1. y = - x2 - 9x + 20

2. y = x2 - 6x + 8 3. y = - x2 - 7x +

10

3. y = x2 + 6x - 8

1. y = x2 + 4x + 3

2. y = –x2 + 4x – 4

1. y = x2 – 1 2. y = –x2 + 2 3. y = x2 - 5 4. y = –x2 + 3