quadratics Flashcards
What is the vertex form of a quadratic?
f(x)=a(x-h)2+k
What is the standard form of a quadratic?
f(x)=ax2+bx+c
What is the factored form of the quadratic?
f(x)=a(x-p)(x-q)
What do h and k stand for in the vertex form?
(h,k) is the vertex
What do p and q stand for in the factored form of a quadratic?
x intercepts
What are the x intercepts from f(x)=2(x-3)(x+4)
(3,0) (-4,0)
What are the x intercepts from f(x)=(2x-3)(x-1)
(1,0) (3/2,0)
What are the x intercepts from f(x)=2x(x-7)
(0,0) (7,0)
What are the x intercepts from f(x)=(x+1)(x-2)
(-1,0) (2,0)
What does c stand for in standard form?
y intercept
What does a tell you in quadratic equations?
if it opens up or down, if it skinny or fat
If a is negative, will the graph open up or down?
down
If a is positive, will the graph open up or down?
up
Give the a, b, c values of the following f(x)=2x2-3x+4
a= 2 b= -3 c=4
Give the vertex from the following equation f(x)=2(x+3)2+4
(-3,4)
When we see (x-3)^2 how do we distribute the 2?
foil
What is the first thing to look for when factoring
greatest common factor
When a>1 how do we start to factor?
multiply a and c
To factor when a=1, do the numbers multiply to b or c?
c
To factor when a=1, do the numbers add to b or c?
b
How do you write equations for axis of symmetry
x=
How do you find the axis of symmetry from standard form?
x= -b/2a
How do you find the axis of symmetry from factored form?
(p+q)/2
How do you find the axis of symmetry from vertex form?
h
What are the two ways we can find the x intercepts from standard form of a quadratic?
quadratic equation, factoring
How do you get from factored form to x intercepts?
set each ( ) = 0 and solve for x
Zero product property
If two things are multiplied together to equal 0, one of the multiplied terms must equal 0
What is the quadratic equation?
What form must the equation be in to use the quadratic equation?
standard
How do we get x intercepts from vertex form?
set y=0 and solve for x
If we get a square root of a negative number, what does that mean?
imaginary x intercepts
If asked for roots what are you finding
x intercepts
If asked for zeros what are you finding?
x intercepts
If asked for the solutions of ab equation when y=0 what are you finding?
x intercepts
What is the x value of the vertex?
axis of symmetry
How do you find the y value of the vertex
plug axis of symmetry in for x in the equation
if a is positive will the vertex be a maximum or minimum?
min
if a is negative will the vertex be a maximum or minimum?
max
What buttons do you press on the calculatorm after you put in the equation to find the max/min
2nd Trace
Where do you put the cursor when the bottom of teh screen says left bound?
to the left of the max/min
Where do you put the cursor when the bottom of teh screen says right bound?
to the right of the max/min
What are the 5 key points needed to graph a quadratic?
y intercept, mirror of y intercept, vertex, 2 x intercept (if any)
Points mirror across what in a quadratic function?
axis of symmetry
if you are mirroring the y intercept, what will the value of the mirrored point be?
the same as the y intercept
How do you find the x value of a mirrored point
The mirrored point is the same distance from the axis of symmetry as the original point
What is the discriminant?
b2-4ac
If there are 2 real x intercepts, what do you know about the discriminant?
discriminant>0
If there are 0 real x intercepts, what do you know about the discriminant?
discriminant<0
If there are 2 real repeating x intercepts, what do you know about the discriminant?
discriminant=0
If there is 1 x intercept, what do you know about the discriminant?
discriminant=0
If the discriminant is<0 what will the graph look like?
The parabola will not cross the x axis
If the discriminant =0 what will the graph look like?
The parabola will touch the x axis, but not cross the x axis
If the discriminant =0 what do you know about the vertex?
The vertex is the x intercept
