unit 4 quiz part 2

Question 1

writing a quadratic equation when given the roots

Answer 1

x2 - sum of rootsx + product of roots = 0

Question 2

to find a double root,

Answer 2

need b2 - 4ac= 0, (discriminant) (one will likely have the x value, so keep it in and then solve for x)

Question 3

standard form for quadratics

Answer 3

ax2 + bx + c

Question 4

vertex form for quadratics

Answer 4

y= a(x-h)2 + k (vertex is h,k)

Question 5

Dx is

Answer 5

ALWAYS all reals of (-infinity, infinity)

Question 6

Ry

Answer 6

EITHER y greater than or equal to the min or less than or equal to the max of the parabola

Question 7

AOS

Answer 7

x coordinate from vertex, can also be found from -b/2a, and in vertex form, the x = h

Question 8

set equation to zero and solve for x

Answer 8

solving for zeros/x intercept

Question 9

plug in x as zero and then solve for y

Answer 9

finding the y-intercept

Question 10

-only use x-values from the graph
- open intervals with (,)

Answer 10

intervals/maxs and mins of graphs

Question 11

find sum/product of roots if they’re not provided

Answer 11

sum: -b/a
product: c/a

Question 12

**roots cannot have denominators so use LCM and multiply them out

Question 13

b2-4ac >0 (NOT a perfect square)

Answer 13

Real, Irrational, Unequal
- graph crosses x acis twice in two irrational points

Question 14

b2-4ac > 0 (perfect square)

Answer 14

real, rational, unequal
- graph touches x axis in two rational points

Question 15

b2-4ac = 0

Answer 15

real, rational, equal (double root)
- graph touches the x axis in one point; tangent to x axis

Question 16

b2-4ac <0

Answer 16

imaginary, the parabola does not touch the x axis

Question 17

when asked to describe nature of roots, if roots are not given, do b2-4ac. when defining the features be careful about which b2-4ac to use

Question 18

to find sum/product of roots (-b/a and c/a) the equation must be in standard form first

Question 19

when the equation asks for a specific max/min value

Answer 19

solve for y value

Question 20

when the problem asks for the time at which a max/min occurs

Answer 20

find x value

Question 21

algabraically- use AOS, find x value, then plug into equation or use calc graph

Answer 21

“At what time does the max/min occur?”

Question 22

if question asks for the time at which an object is at a gven height, look for x value. set equation equal to given height

Question 23

if the questions asks for the time at which an object hits the ground, set equation to zero to find roots (or graph?)

Question 24

(x-h)2 = 4p (y-k)

Answer 24

locus formula of a parabola

Question 25

parabola= collection of all the points equidistant from focus & directrix

Answer 25

when solving, change from locus to standard form (then you can check with calc)

Question 26

positive vs negative leading coefficient

Answer 26

if there is a negative leading coefficient, the locus equation NEEDS to be negative. so the equation becomes -(x-h)2 = 4p (y-k)

Question 27

completing the square: any leading coefficients in x2 are factored out from the start, so the same value is added in the parenthesis and subtracted out of it. the constant is added to the side of 0 so the (x + 1)2= that number, then it’s squared, so the final answer is that x equals something. it also FOLLOWS THROUGH WITH THE b/2 squared thing.

Answer 27

steps to writing quadratic equations in vertex form by completing the square

Question 28

if there’s a leading coefficient, it’s simply placed outside the parenthesis and the numbers inside the parenthesis are adjusted to it. the third value is taken from the 2nd one (b/2)2, and depending on how big the value is outside the parenthesis, the constant number (that ‘ll be subtracting the number) is adjusted (unlike completing the square where it stays constant) after, the equation is set up so the leading coefficient is outside the parenthesis, then (x, then plus or minus based on the first equation, then the squared value of the third number in the parenthesis, so for example the end result looks like 2(x + 2)2 + 4 and the vertex would be -2 and 4.

Answer 28

changing from standard to vertex form (NOT completing the square)
the final answer is expressed as y= (x-h)2 + k and vertex stated as (h,k)

Question 29

use b2-4ac for roots (when graph touches x axis) and -b/2a for AOS, finding x value for a vertex

Question 30

Nature of roots

Answer 30

Discriminant

Question 31

Algabraically finding the set of x intercepts for parabolas

Answer 31

B2-4ac