# Algebra 2 Concepts Flashcards

Why are they called “quadratics?”

It comes from the Latin word “quadrus” which means SQUARE

What is the tough thing about quadratics?

The fact that they are squared.. We have to undo that x2. We want to get it linear!!

How do we handle that squared term? how can we undo it?

By either splitting the x’s apart by factoring, or by taking a square root somewhere..

Why is it called a “linear” term

It creates a straight line when graphed

Why is it called a constant term

Alone it would be a constant function.. The same height always. a horizontal line with a constant y, a constant height

Why is it called a discriminant?

Because it discriminates between which type of solutions, roots and zeros you will have (2real, one real or imaginary)

Are all quadratics similar?

YES.. THEY ALL HAVE THE EXACT SAME SHAPE.. They are simply zoom-ins or zoom-outs of eachother..

Why do parabolas look different if they are all similar?

Well…. Simply either imagine zooming way in or zooming way out… this method can always get any 2 parabolas to look the same.

f(x)= 3x2-4x+5 What is a, b and c ?

a = 3, b = -4, c = 5

How do you know when it is a quadratic?

When the highest degreed term is the x2 term (quadrus:square)

f(x)= 3x2-6x+3 What is the quadratic term?

3x2

f(x)= 3x2-6x+3 What is the linear term?

-6x

f(x)= 3x2-6x+3 What is the constant term?

3, it is the also the y intercept

What is a coefficient?

The number in front of a variable or variables

f(x)= 3x2-6x+3 What is the coefficient of the quadratic term?

3 this is also known as “a”

f(x)= 3x2-6x+3 What is the coefficient of the linear term?

-6 this is also known as “b”

f(x)= 3x2-6x+3 What is the coefficient of the constant term?

3 this is also known as “c”

What is the quadratic term’s exponent on the x ?

2

What is the linear term’s exponent on the x ?

1

What is the constant term’s exponent on the x?

0

f(x) = ax2 + bx + c What is the coefficient of the quadratic term?

a

f(x) = ax2 + bx + c What is the coefficient of the linear term?

b

f(x) = ax2 + bx + c What is the coefficient of the constant term?

c (it is the y intercept)

f(x) = ax2 + bx + c What is the quadratic term?

ax2

f(x) = ax2 + bx + c What is the linear term?

bx

f(x) = ax2 + bx + c What is the constant term?

c (it is the y intercept)

Describe what an axis of symmetry is

it is where the parabola can fold onto itself. It is the equation of this vertical line, so you write “x = ___”(-b/2a)

What is the equation of the axis of symmetry?

x = -b / 2a(notice it is the equation of a vertical line) (also Notice it is hidden in the quadratic formula)

Where is the vertex located?

On the axis of symmetry (highest or lowest point)

What is the quadratic formula?

x = -b +- sqroot b squared - 4ac all over 2a (but in formula)

What is the discriminant?

b2-4ac (notice there is no sq root on it!!)

What does the discriminant tell us about?

About the roots, the zeros, how many x intercepts the parabola has, how many times it crosses the x axis, whether roots are real or imaginary

What do we call b2-4ac

The discriminant

Why are roots called “zeros”

Because it is where the height is zero; where the y value is zero; they are the x values that make the y=0

What is difference between (3, -2) and {3, -2}

The first is a point on a plane (over 3, down 2) and is in parentheses… The second set are numbers in braces, so it is simply a set containing two values, 3 and -2. It is not a point on a plane, the order does non matter in braces.

What are the roots of a function? (other names?)

The zeros, the x-intercepts, the solutions,where the parabola crosses

What are the zeros of a function? (other names?)

The roots, the x intercepts, the solutions, where the parabola crosses

What are the solutions of a function? (other names)

The roots, the x intercepts, the zeros where the parabola crosses

What are the x intercepts of a function? (other names?)

The roots, the zeros, the solutions

What are the three common forms of quadratic functions?

Standard form, vertex form, and factored form (factored form can be called zero form or root form)

What is the Vertex form of a quadratic?

f(x) = a(x-h)2 + k

What is the Factored form of a quadratic?

f(x)=a(x-r)(x-r)

what is tricky about the Vertex form?

the -h part.. If its (x+9)2 +8 then h is -9.. remember that h is also the AOS !!!

What is the Standard form of a quadratic?

ax2+bx+c = 0

f(x) = a(x-h)2 + k How do we know if it opens up or down?

by the sign of a, if its positive, up, negative , down

How do you know when a parabola is smiling?

when a is positive

How do you know when a parabola is frowning?

when a is negative

How is the axis of symmetry hidden in the quadratic formula?

it is the beginning.. (put both parts over 2a)

Do all quadratic functions have x intercepts?

No, some don’t touch the x axis.. These have imaginary roots and a negative discriminant

Do all quadratics have a y intercept

YES… All quadratics have exactly 1 y-intercept.. (c).. if there is no constant term, the y intercept is 0, so the parabola passes through the origin!!!!