Vertex Form
Where is the vertex?
f(x) = -(x + 3)2 - 1
(-3,-1)
What is the equation for the line of symmetry:
y = 3(x - 2)2 + 10
x = 2
Where is the y-intercept?
f(x) = x2 + 2x - 10
(0,-10)
What is the GCF: 3x3 - 12x
3x
Write a vertex Form equation that does not have any real zeros.
What is the pattern:
y = -2x2 - 8
-2, -6, -10, ...
y= -x2 + 3x + 5
-1, -3, -5, ...
Factor out the GCF:
2x2 - 10x
2x(x - 5)
Write in vertex form by completing the square:
f(x) = x2 - 10x + 14
f(x) = (x - 5)2 - 11
What is the domain and range in interval notation:
y = -(x + 5)2 + 7
Domain: (-infinity, infinity)
Range: (-infinity, 7]
Rearrange into standard form:
y= (x + 1)2 - 6
y = x2 + 2x - 5
Factor:
x2 + 14x + 28
(x + 12)(x + 2)
Write the equation below in vertex form by completing the square:
f(x) = 2x2 + 4x - 6
f(x) = 2(x + 1)2 - 8
Where is the line of symmetry?
y = x2 + 6x - 11
x = -3
Rearrange into standard form:
y= 1/3(x - 9)2
y = 1/3x2 - 6x + 27
Factor:
x2 - 25
(x + 5)(x - 5)
Write the equation below in vertex form by completing the square:
y = -1/3x2 + 4x - 1
How many real zeros does the parabola have? Explain how you know.
y = 2x2 + 8x + 10
The vertex is at (-2,2) [above the x-axis] and is concave up, so the parabola would not touch the x-axis. It has no real zeros.
Rearrange into standard form:
y = 2/5(x + 10)2 - 8
y = 2/5x2 + 8x + 32
Factor:
2x2 - 4x - 6
2(x + 1)(x - 3)