Key Parts of the Parabola
Basic Quadratic Equations
Graphing a Parabola
Parabolas in every day life
BONUS QUESTIONS
100
Define vertex
The vertex is a point in which the parabola reaches its maximum or minimum height
100
What are two forms of a quadratic relation
1) Standard form
2) vertex form
100
What are some of the key parts of a parabola (give at least 3)
Maximum, minimum,optimum value, vertex, zeros, axis of symmetry,, x-int, y-int
100
What is standard form of a quadratic?
f(x)=ax2 +bx+c
100
without knowing the equation how can you tell if a parabola is positive or negative just by looking at the graph?
If its curving up and is resembling a happy face the parabola would be positive:
And if the curve is the opposite of this, curving downwards and resembling a sad face it would be negative
* way to remember: sad is a negative feeling
happy is a positive feeling
200
Parabolas are like butterflies because they are....
symmetric!
200
Which form is represented by the equation ax^2+bx+c
Standard form
200
How do you graph a parabola from vertex form?
Y=2(x-2)2+18
You will start at the at the vertex which in this case is (2,18) and then symmetrically substitute the values of x in the function
200
What are some ways we use parabolas in everyday life?
kicking a soccer ball, fish jumping out of the water, our teeth...
200
State the vertex, zeros, optimum (maximum/minimum) value and whether the parabola is positive or negative (the direction of opening)
Vertex: (2,1)
Zeros: 1 and 3
Optimum value: -3
Direction of opening: parabola is travelling downwards therefor it is negative
300
Define the axis of symmetry
The axis of symmetry is is parallel to the y-axis and it passes through the vertex; in other words it divides the parabola in half.
300
The vertex form equation
What is f(x)=a(x-h)2+k
300
How can you tell the difference between an equation of a line and a quadratic?
The squared term! y=x versus y=x^2
300
In a parabola that is representing a ball being thrown, what tells us when the height of release is?
the y-intercept
300
If you don't have a graph just an equation how can you determine the direction of opening?
the step pattern:
Y=-2(x+4)2+4
if the value of "a" is negative then the parabola will be opening downwards, if positive, upwards.
400
how do you determine if a parabola is going to have a maximum or minimum
If the parabola opens upward, it is a minimum. If it opens downward, it is a maximum.
400
What forms are the equations given below written in
1) Y=2(x-3)2+62
2) Y=4x2+6x+10
1) Vertex form
2) Standard form
400
What are the effects of the "a" value on a parabola?
It tells us if the parabola is going to open upward or downward
400
What do the zeros tell us in a graph of a soccer ball being kicked?
When the ball left the ground and when it came back
400
How many x-intercepts can a quadratic functions have and why
0, 1 and 2
500
State the zeros in the given graph below and give the definition
The zeros are -1 and +3
Zeros are where the parabola crosses the x-axis.
500
Write the equation of a parabola that has a vertex of (-4,9) and is concave up
y=(x+4)2+9
500
Is parabola a decreasing or an increasing function? What defines it?
Both. If it has minimum, then it firstly decreases, and then increases. If it has maximum, then vice versa
500
a football player kicks a ball off a football tee. The height of the ball,h, in meters after t seconds can be modeled using the formula: h=-5t2+20t. Create a table of values for this relationship. Use x=-2,-1,0,1,2
t h
-2 -60
-1 -25
0 0
1 15
2 20
500
Do the equations listed below represent a quadratic relation? Why or why not, explain.
1) y=2x+3
2) y=2(x-5)(x+6)
1) this equation does not as it is in y=mx+b form which would create a line not a quadratic
2) this equation does because it is in factored form therefor it creates a parabola