Quadratics in Standard Form
Quadratics in Vertex Form
Mixed Bag
Convert to Standard
Convert to Vertex
100
The standard form of quadratics
y=ax^2+bx+c
100
The vertex form of quadratics
y=a(x-h)^2+k
100
Write the vertex form of the quadratic
y=-(x+2)^2+1
100
Convert to standard form:
y = (x-2)2+4
y = x2-4x+8
100
The process to convert quadratics in standard form to quadratics in vertex form
completing the square
200
Calculate the x-value of the vertex of
y = x2-10x+6
x= 5
200
Vertex of
y = a (x - h)^2 + k
(h, k)
200
Find the axis of symmetry of
y=-2x^2 + 16x + 4
x=4
200
The first step in converting a vertex form into standard form (i.e. converting y=2(x-4)2+3)
Distribute (x-4)(x-4)
200
Rewrite into vertex form:
y = x2-12x+34
What is the vertex?
y = (x-6)2-2
(6, -2)
300
Calculate the x-value of the vertex of:
f(x) = 2x2+8x-3
x= -2
300
The vertex of
f(x)=-2 (x - 4)^2 + 2
(4,2)
300
Write the equation of a quadratic that has a vertex of (1, 2) and goes through the point (3, 10).
y = 2(x-1)2 + 2
300
Convert to standard form:
y = (x+3)2-4
y = x2+6x+5
300
Rewrite into vertex form:
y = x2-10x+19
What is the vertex?
y = (x-5)2-6
(5, -6)
400
Find the vertex:
y = 5x2+15x+6
(-1.5, -5.25)
400
The Vertex of
y = 2(x-3)^2 - 8
(3, -8)
400
The height of a basketball shot in meters can be represented by
y=-4t^2+8t+3
where t represents seconds since the shot was taken.
What is maximum height (in meters) of the basketball?
7 meters
400
Convert to standard form:
f(x) = 2(x-2)2+2
y = 2x2-8x+10
400
DAILY DOUBLE!!
Rewrite into vertex form:
y = 2x2-8x+8
What is the vertex?
y = 2(x-2)2
(2, 0)
500
Find the vertex:
y = -2x2-12x+15
(-3, 33)
500
DAILY DOUBLE!!
Describe the transformations from the parent function:
y = -4 (x + 6)2 - 4
reflection across the x-axis, vertical stretch by a factor of 4, shifted left 6, shifted down 4
500
DAILY DOUBLE!!
The maximum height (in feet) of a rocket that can be modeled by the following
y=-2x^2-26x
84.5 feet
500
Convert to standard form:
y = -3(x+7)2 + 40
y = -3x2-42x-107
500
Rewrite into vertex form:
y = 3x2-18x+40
What is the vertex?
y = 3(x-3)2+13
(3, 13)