Quadratics in Standard Form
Quadratics in Vertex Form
Conversions
Graph
Modeling
100
The standard form of quadratics
y=ax^2+bx+c
100
The vertex form of quadratics
y=a(x-h)^2+k
100
Does the graph of
-2(x + 5)2 + 2 open upwards or downwards?
Downwards
100
What is the name for the graph of a quadratic equation?
parabola
100
What is the formula for a quadratic equation modeling vertical motion?
-16t2 + v0t + h0
200
The value of y -intercept of quadratics in standard form
y=c
200
A parabola has a vertex at (-3,2). Where is the axis of symmetry?
x = -3
200
The values of a that reflect (turn upside down)
y = a (x - h)^2 + k
a < 0
200
What is the y-intercept of this graph?
(0, 5)
200
The height of a thrown football is modeled by the equation h(t) = -16t2 + 12t + 6. What was its initial upward velocity?
12 feet/second
300
Find the axis of symmetry of
y = x2 - 6x + 13
x = 3
300
What is the vertex of the equation
y= (x-12)2+7 ?
(12, 7)
300
When x2 is changed to x2 -3, what happens to the graph?
Shifts down 3 units.
300
What is the vertex of this graph?
(2, 1)
300
Write a quadratic expression for the area of a rectangle with side lengths (x + 3) and (x - 2).
x2 + x - 6
400
The y-value of
y = x^2 + 2x + 1 at
x=-4
y=9
400
The vertex of
-2 (x + 4)^2 + 2
(-4,2)
400
When x2 is changed to 0.5x2, how does the graph change?
It gets wider by a factor of 2.
400
Write an equation for the graph. (Hint: the graph has not been stretched or compressed)
y = -(x - 2)2 + 4
400
A basketball is thrown straight up in the air from an initial height of 2.1 feet at an initial velocity of 7 feet per second. Write a function that models the height of the basketball after t seconds.
-16t2 + 7t + 2.1
500
Convert y = 2(x + 3)2 - 5 into standard form.
y = 2x2 + 12x + 13
500
The y -intercept of
y = 2(x+3)^2 - 8
y=10
500
Transformation(s) of
-4 (x + 6)^2 - 4
1. vertical stretch by a factor of 4
2. vertical shift 4 units down
3. horizontal shift 6 units left
4. vertical reflection (flipped upside down)
500
Write an equation for the graph in standard form. (Hint: a = 1)
y = x2 - 6x + 8
500
A painting has a width of x inches and a height of 2x inches, and it has a 1-inch thick frame on each side. Write an equation for the area of the painting including the frame.
2x2 + 6x +4