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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