DECK 2: QUADRATIC TERMS INTRO

Question 1

What is the shape of a quadratic graph called?

Answer 1

A parabola

Question 2

What is the highest or lowest point (x,y) called on a parabola? It is on the AOS. It is sometimes written as (h,k)

Answer 2

The vertex.

Question 3

Is the vertex of a parabola always on the axis of symmetry?

Answer 3

YES. The x value of the vertex is the axis of symmetry.

Question 4

What is the axis of symmetry?

Answer 4

It is the vertical line that goes through the middle of the parabola- parabola folds on itself. THE VERTEX IS ON IT

Question 5

What does VERTICAL mean?

Answer 5

Up and Down

Question 6

What does the line x = 10 look like?

Answer 6

A vertical line through 10 on the x axis

Question 7

What is the equation of a vertical line through 7 on the x axis? (visualize a vertical line through 7 on the x axis)

Answer 7

x = 7
All vertical lines have equation
“ X = some number”

Question 8

Since the axis of symmetry is a vertical line, the equation of the axis of symmetry is always:

Answer 8

X = some number

you have to write “x = ? “

Question 9

What does HORIZONTAL mean?

Answer 9

Left and right

Question 10

Do all parabolas have x-intercepts? If so, how many?

Answer 10

NO - they may have
NONE, ONE or TWO.

Question 11

Do all parabolas have y-intercepts? If so, how many?

Answer 11

YES, they all have EXACTLY ONE y intercept.

Question 12

How can a parabola have no real roots (no x intercepts)?

Answer 12

If it doesn’t touch the x axis. Smiling parabola above, or frowning parabola below.

Question 13

How can a parabola have only one real root (one x intercept)

Answer 13

If it touches the x-axis only at one point (the vertex) and “bounces off”

Question 14

How can a parabola have two real roots (two x intercepts)

Answer 14

If it crosses twice.

Question 15

How do you find the y intercept for any linear or quadratic function?

Answer 15

Set X=0 and solve for y

Question 16

How do you find the x-intercepts of any linear or quadratic functions?

Answer 16

Set Y=0 and solve for x (this involves setting each factor = 0 and solving for x for each)

Question 17

What are the three forms of quadratic functions?

Answer 17

standard, vertex and factored (intercept) forms

Question 18

What form?
f(x)=ax ² +bx+c

Answer 18

Standard

Question 19

What is the standard form of a quadratic?

Answer 19

f(x)=ax ² +bx+c

Question 20

What form?
f(x) = a(x-h) ² +k

Answer 20

Vertex form

Question 21

What is the vertex form of a quadratic?

Answer 21

f(x) = a(x-h) ² +k

Question 22

What form?
f(x)=a(x-Z)(x-Z)

Answer 22

Intercept or Factored form

Question 23

What is the intercept (factored) form of a quadratic?

Answer 23

f(x)=a(x-Z)(x-Z) where Z and Z are ZEROS, roots, x-intercepts

Question 24

For any polynomial in factored form, how do you find the ROOTS, ZEROS, SOLUTIONS, X-INTERCEPTS?

Answer 24

SET THE FACTORS EQUAL TO ZERO AND SOLVE!
EX: f(x)=3 (x-5)(x+10) Roots are 5 and -10
because (x-5)=0 when x=5
and (x+10)=0 wnen x=-10
You can often do the math in your head. But if a factor is (3x-5), you would have to solve for
x in 3x-5=0

Question 25

What does "a" tell us about the graph?

Answer 25

Two things. If it is + it smiles, if it is - it frowns AND if a>1 (bigger than 1) it gets narrow. If a <1 (smaller than 1) it is WIDE

Question 26

Is "a" the same for all three forms?

Answer 26

Yes, whatever "a" is in standard form, it will be the same value in factored and in vertex form. It always tells us + SMILE, -FROWN, bigger than 1 it gets NARROW, and smaller than one it gets WIDE

Question 27

What if you have +a value?

Answer 27

Concave UP, smiling

Question 28

What if you have -a value?

Answer 28

Concave DOWN, frowning

Question 29

How do you know when a parabola is smiling?

Answer 29

when a is positive

Question 30

How do you know when a parabola is frowning?

Answer 30

when a is negative

Question 31

What are the three forms of a quadratic function and their equations?

Answer 31

Standard y=ax ² +bx+c Vertex y=a(x-h) ² +k Factored y=a(x+f)(x+g)

Question 32

What is the GIFT you get in standard form?

Answer 32

The y intercept. It is at C or (0,c)

Question 33

What is the GIFT that you get in vertex form?

Answer 33

The vertex (h,k). This also give you the AOS and the MAX/MIN

Question 34

What is the GIFT that you get in factored form?

Answer 34

The x intercepts - the ZEROS- the ROOTS.

Question 35

WHAT FORM and WHAT IS THE GIFT? f(x)= -2x²-4x+9

Answer 35

Standard Form GIFT Y intercept at (0,9)

Question 36

WHAT FORM and WHAT IS THE GIFT? f(x)= -2(x+7)²+11

Answer 36

Vertex Form GIFT Vertex at ( -7, 11)

Question 37

WHAT FORM and WHAT IS THE GIFT? f(x)= -2(x+9)(x-11)

Answer 37

Intercept/Factored Form GIFT X-intercepts at -9 and 11 or (-9,0) and (11,0)

Question 38

f(x)=2x ² -4x+6 What is the y intercept?

Answer 38

(0,6)

Question 39

f(x)=2(x-5)(x-3) What are the x intercepts?

Answer 39

At 5 and at 3

Question 40

f(x)= 2(x+4) ² -3 What is vertex?

Answer 40

(-4, -3)

Question 41

If you have a vertex, like (5.10), what else do you have?

Answer 41

The AOS and MAX/MIN. The AOS is at x=5 and the max/min is y=10

Question 42

y=-2x ² -4x+6 concave up or concave down?

Answer 42

a= -2 concave DOWN

Question 43

f(x)=2(x-5)(x-3) concave up or concave down?

Answer 43

a=2 concave UP

Question 44

f(x)= -3(x+4) ² -3 concave up or concave down?

Answer 44

a= -3 concave DOWN

Question 45

If we know the coordinates of the vertex is always (AOS, MAX/MIN), then if a vertex is at (5,12), WHAT OTHER INFORMATION DO WE KNOW?

Answer 45

We know the AOS is at x=5 and the max/min is at y=12

Question 46

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

Answer 46

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

Question 47

If a parabola is concave up, smiling, will it have a MAX or MIN?

Answer 47

IF it is smiling, it goes up forever, so it has no max value IT ONLY HAS A MIN Y VALUE

Question 48

If a parabola is concave down, frowning, will it have a MAX or MIN?

Answer 48

If frowning, it goes down forever so it has no minimum, IT ONLY HAS A MAX Y VALUE

Question 49

f(x)= 2(x+4) ² -3 What is vertex ?

Answer 49

at (-4, -3), SMILING so it opens upwards, -3 is a MIN value

Question 50

f(x)= (x+9)²-8 What is vertex

Answer 50

at (-9, -8)

Question 51

f(x)=2(x-5)(x-3) What are the ROOTS?

Answer 51

5 and 3

Question 52

y=2(x-7)(x+3) what are the coordinates of the x intercepts?

Answer 52

(7,0) and (-3,0)

Question 53

How do we know when to take opposites when working with quadratics?

Answer 53

usually when they are in parentheses

Question 54

Suppose a vertex of a parabola is at (5,10), what else do you know?

Answer 54

You know the AOS is at x=5 and the max/min is at y=10.

Question 55

If a vertex is at (8, -9) and frowning, what do you know?

Answer 55

You know the AOS is at x=8 and the MAX value is y=-9 FROWNS HAVE MAXIMUM HEIGHTS BUT GO DOWN FOREVER

Question 56

If a vertex is at (5, 12) and smiling, what do you know?

Answer 56

You know the AOS is at x=5 and the MIN value is y=12 SMILES HAVE MINIMUM HEIGHTS BUT GO UP FOREVER

Question 57

What is the word for a line that goes left and right?

Answer 57

Horizontal line

Question 58

What is the word for a line that goes up and down?

Answer 58

Vertical line

Question 59

What is the equation of a horizontal line through the y axis that is up 5

Answer 59

y=5

Question 60

What is the equation of the vertical line that is over to the left at -10 on the x axis?

Answer 60

x= -10

Question 61

what does "a" tell us in this quadratic? f(x)= -5(x-3)²+13 TWO THINGS

Answer 61

It is - so frowning 5 makes it NARROW

Question 62

What does "a" tell us in this quadratic? f(x)= 0.25(x-3)²+13 TWO THINGS

Answer 62

It is + so smiling, and 0.25 makes it wide.