Parabolas Flashcards
What is a Stretch Factor? Where is it located in an equation?
The number in vertex form before the brackets, that decides by what factor the parabola is stretched by.
*WRITTEN AS A=2*
Example: 2 (x-3) 2+8
What are x- intercepts? Where are they located in an equation?
The numbers inside the brackets in factored form, of the opposite sign (+,-) where a parabola intersects on the x axis in two places.
Example: y= (x+4) (x+2)
x-intercepts: -4 and -2
What is a Y-intercept? Where is it located in an equation?
The number at the end of a standard form equation that shows where a parabola intersects on the y axis.
*WRITTEN AS (0,?)
Example: y= x2+6x+8
Y-intercept: (0,8)
What is the Axis of Symmetry? Where is it located in an equation?
The number inside the brackets of standard form equation,of the opposite sign, that shows where the parabola is split in half equally on the x axis. It also shows whether the parabola shifts left or right.
*WRITTEN AS X=?*
Example: -2 (x-3)2+8
x=3
What does a Maximum Parabola look like?
A parabola that opens down
What does a Minimum Parabola look like?
A paraboa that opens up
What is an Optimum Value? Where is it located in an equation?
The number located at the end of a vertex form equation that shows whether a parabola shifts up or down.
*WRITTEN AS Y=?*
Example: y=(x+3)2 **-1 **
Optimum Value: y= -1
What is a Vertex? Where is it located in an equation?
The numbers located as the number in brackets and the number outside of the brackets in a vertex form equation. It shows the of the curved part of the parabola.
*THE NUMBER INSIDE THE BRACKETS BECOMES THE OPPOSITE SIGN*
*WRITTEN AS (?,?)*
Example: y= (x+3)2 -1
Vertex= (-3,-1)
How do you Descirbe a Transformation?
Step 1) See if there is a negative stretch factor
Example: y= -2 (x+3)2 -1
In your transformation write “Reflects in the X-axis”
Step 2) See if there is a stretch factor
Example: y= -2 (x+3)2 -1
In your transformation write “Stretches by a factor of 2”
If the stretch factor is a fraction, write “Compresses by a factor of ?”
Step 3) Identify if the parabola shifts left or right (opposite sign)
Example: y= -2 (x+3)2 -1
In your transformation write “Shifts 3 units left”
Step 4) Identify if the parabola shifts up or down
Example: y= -2 (x+3)2 -1
In your transformation write “Shifts 1 unit down”
How do you graph a parabola?
Step 1) Plot the vertex
Step 2) Move over one up one from the vertex
Step 3) Move over 2 up 4 from the vertex
Step 4) Repeat on the opposite side to make the parabola symmetrical
*STRETCH FACTOR: MULTIPLY EACH STANDARD PLOT BY THE STRETCH FACTOR*
* IF THERE IS A NEGATIVE SIGN, THE PARABOLA OPENS IN THE OPPOSITE DIRECTION*
What is the General Equation for a Quadratic Relation?
y= a(x-h)2+k
What is the Quadratic Formula?
What is the equation to find the vertex?
How do you find the x intercepts of a parabola?
Factor or use the Quadratic Formula; The 2 factors, or 2 answers from the quadratic formula are the x-intercepts
Write the equation of the parabola that, compared to y= x2 is opening down, stretched by a factor of 1/3, and has a vertex that is shifted 4 left and 5 down.
y= -1/3 (x+4) 2 -5
