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. Where the two sides of the parabola meet.
100
What are two forms of a quadratic function
1) Standard form
2) vertex form
100
What are some of the key parts of a parabola (give at least 3)
Maximum, minimum, 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 the parabola would be positive:
And if the curve is the opposite of this, curving downwards, it would be negative
200
The y-value of the vertex is called the...
maximum value
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 pick two x-values on the same side of the vertex to plug into the equation and find the y-values. Plot the points and make the mirror image on the other side.
200
What are some ways we use parabolas in everyday life?
kicking a soccer ball, fish jumping out of the water
200
State the vertex, zeros, maximum/minimum value and whether the parabola is positive or negative (the direction of opening)
Vertex: (2,1)
Zeros: 1 and 3
Maximum value: -3
Direction of opening: parabola is travelling downwards therefore it is negative
300
Define the axis of symmetry
The axis of symmetry is the vertical line that 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 do you graph a parabola from standard form?
Y=-2x^2+2x+2
Start by finding the axis of symmetry x=-b/2a. Then use what x equals and plug it into the equation to find the y-value of the vertex. Plot the vertex, Pick two x-values on the same side, next to the vertex. Plug them into the equation. Plot those points, create the mirror image.
300
In a parabola that is representing a ball being thrown, what part of the parabola tells us when the ball is released?
the y-intercept
300
A soccer ball is kicked and follows a path modeled by the function f(t)=-16t(t-5). What is the maximum height the ball reaches?
It will reach the max height at 100 feet.
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. It can also tell us if the parabola is narrow or wide.
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
A soccer ball is kicked and follows a path modeled by f(t)=-16t(t-5). How long is the ball in the air?
The ball is in the air for 5 seconds.
500
State the zeros in the given graph below and give the definition
The zeros are -2 and +2
Zeros are where the parabola crosses the x-axis.
500
Write the equation of a parabola that has roots of 1 and 3 and passes through the points (2, -3). Be sure to find a, it may or may not be -1 or +1.
y=3x2-12x+9
500
Identify the vertex from the graph? How many zeros does the quadratic have? Is "a" positive or negative?
vertex: (-2,5)
2 zeroes
"a" is negative
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. Find how long it takes for the ball to reach it's max height. Also find what the max height is.
It takes 2 seconds to reach the max height of 20 meters.
500
Do the equations listed below represent a quadratic equation? 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 parabola
2) this equation does because it is in factored form therefore when you distribute the binomials, it will create the highest degree of x^2, making it quadratic and it creates a parabola