Standard Form
The standard form of quadratics
y=ax^2+bx+c
The vertex form of quadratics
y=a(x-h)^2+k
What is the parent function of a quadratic?
y=x^2
Quadratic equations take the shape of a what when graphed.
u
Describe the transformation(s):
y=x^2-7
Down 7
The y-value of
y=-3x2-2x+1 at x=-4
y=-39
What does a vertex represent in terms of a graph?
Does the graph of
-2(x + 5)2 + 2
have a minimum or a maximum?
Maximum
Graph the following and give the axis of symmetry:
y= x^2 + 2
x = 0
Describe the transformation(s):
y=1/2(x+3)^2
Compression by 1/2
Left 3
The y-value of
y = x^2 + 2x + 1 at
x=0
y=1
The vertex of
y=-2 (x + 4)^2 + 2
(-4,2)
Find the vertex:
y=-6x2+1
(0,1)
The vocabulary word for the curve of a quadratic is called a.....
Parabola
Describe the transformation(s):
y=-(x-2)^2 + 5
Reflected/Flipped Over X-Axis
Right 2 and Up 5
What is the vertex of the following function
y=3x2+4x-6
(-0.7, -7.3)
what is the vertex? and does it open up or down?
y = 2(x+3)^2 - 8
(-3,8) opens up
A parabola has a vertex at (-3,2). Where is the axis of symmetry?
x = -3
What is the maximum or minimum value of the following graph:
y=1/2(x+2)^2-3
Minimum Value = -3
Write the Equation:
Translated 3 units down
y= x^2-3
What is the vertex? Does it have a min or max value?
y=-4x^2-48x-128
(-6,16) and max value
A scientist found that for the years 2012-2018, the equation models the average gas mileage of used vehicles sold in Florida, where x is the number of years since 2012 and y is the average gas mileage. Enter a number to show the year when the average gas mileage was the greatest for used vehicles sold in Switzerland.
y=-0.4(x-3)^2+42
2015
What formula do you use when the quadratic is in standard form and you need to find the AOS?
x=-b/2a
Graph and determine the Domain and Range:
y=x^2-4x-3
Domain: All Real Numbers
Range:
y>=-7
Write the Equation:
Vertically stretched by 2, then translate 4 units left and 1 unit down
y=2(x+4)^2-1