Vertex Form
If a = -2 h = -3 k = -4 How do you write
the equation in vertex form?
y = -2 ( x + 3 )2 - 4
What is the standard form of a quadratic function?
f(x)=ax2+bx+c
Convert y = 3( x +2 )2+ 6 to standard form
y=3x2+12x+18
Consider:
f(x)=2(x+4)(x-8)
What are the x-intercepts?
What is the axis of symmetry?
x-intercepts: -4, 8
Axis of symmetry: 2
How is a graph translated when you add 3 to the input of the parent function?
The graph is translated 3 units to the left.
Convert y = x2 - 2x +3 into vertex form
y = ( x - 1 )2 + 2
[y = (x2-2x+1)-1+3]
What is the y-intercept for the function
f(x) = 3x2 - x -11?
(0, -11 )
Complete the Square to convert y = x2 + 8x - 1 into
vertex form.
y=(x+4)2-17
What is the value of "c" that completes the square for x2 + 13x
vertex: (2,-72)
y-intercept: -64
How is a graph translated when you add -4 to the output of the parent function?
The graph is translated 4 units down.
What is the vertex of the following function?
y = - ( x + 2 )2 - 3
(-2,-3)
Which of the following is true with respect to the
functions f(x) = x2 -5x + 10 and f(x) = -3x2 -3x + 10 ?
A They have the same vertex
B They have the same range
C They have the same y-intercept
D All of the above
C . They have the same y-intercept
Convert to vertex form by completing the square:
y = x2 - 18x + 82
y = ( x - 9 )2 +1
Consider:
f(x)=(x-3)(x-5)
What is the vertex?
What is the y-intercept?
vertex: (4,-1)
y-intercept: 15
How is a graph translated when you multiply 5 by the output of the parent function?
The graph results in a vertical stretch by a factor of 5.
What is the vertex of y = ( x - 2 )2 -7?
(2,-7)
Which of the following functions has a parabola that opens upward? y = 1/2 x2 - 2x +10
y = -1/10 x2 +20x -10
y = 1/2 x2 - 2x +10
Convert to vertex form: y = x2 +12x +18
y = ( x +6 )2-18
Consider:
f(x)=(x-3)(x-5)
What are the x-intercepts?
What is the axis of symmetry?
x-intercepts: 3, 5
axis of symmetry: 4
What is the equation of the parent function moved right 6 units, translated up 3 units and vertically
compressed by 0.91?
y = 0.91( x - 6 )2 +3
Given the vertex of (-2, 5 ) what is the equation in vertex form?
y = ( x +2 )2 +5
Consider: y = 3x2 +12x +6
Name the axis of symmetry and the y-intercept
axis of symmetry: x=-2
Convert to vertex form: y = x2 - 6x + 2 ?
(x-3)2-7
Convert to vertex form by completing the square:
y = x2 - 18x + 82
y = ( x - 9 )2 +1
What is the equation that results from
y = 2 ( x - 6 )2 +3 and translating it 9 units left
and 4 units down?
y = 2 ( x +3 )2 - 1