Quadratic parabolas

Question 1

Expand a perfect square
(x+a)(x+a)

Answer 1

do first one squared
then two times the two multiplied together
then the second one squared
x^2 + 2ax + a^2

Question 2

How to factorize (x+6)(x+2)

Answer 2

x(x+2)+6(x+2)

Question 3

Factorizing with four terms

Answer 3

group them into pairs with the same expression in the brackets. then use one of the brackets with the two numbers outside
ax^2 +ax+2x+2
ax(x+1)+2(x+1)
(x+1)(ax+2)

Question 4

Factorizing quadratic trinomials

Answer 4

Find two numbers that when added together equal the coefficient of bx and when multiplied together equal c.
x^2 +7x+6 –> (x+1)(x+6)

Question 5

Distributive law

Answer 5

a(b+c)=ab+ac

Question 6

FOIL

Answer 6

First outer inner last

Question 7

Product of conjugates (a+b)(a-b)

Answer 7

(a+b)(a-b) = a^2-b^2

Question 8

equation of a verticle line

Answer 8

x= a number

Question 9

Quadratic function

Answer 9

f(x)=ax^2 + bx + c
a,b,c are fixed numbers
c is the y intercept
x, f(x) are variables
f(x) = y

Question 10

What is the min/max point of a parabola called

Answer 10

the vertex

Question 11

how many x intercepts are there on parabola

Answer 11

2

Question 12

what is the axis of symmetry

Answer 12

the line that goes through vertex
x= a number

Question 13

How to find x intercepts from a standard form quadratic function

Answer 13

rearrange the function so it is
ax^2 + bx + c = 0
then find the numbers that when added together equal b and when multiplied equal c. the opposite sign of those numbers are the x intercepts

Question 14

how does c affect parabola

Answer 14

how up/down it is

Question 15

how does b affect parabolas

Answer 15

how left to right it is

Question 16

how does a affect parabola

Answer 16

how narrow/wide and if it is concave up or concave down

Question 17

Vertex in each form

Answer 17

Vertex form = h and k
standard form = (-b/2a), f(-b/2a)
Factored form = expand then use standard form method

Question 18

axis of symmetry from each form

Answer 18

Vertex form = h
standard form = (-b/2a)
factored form = expand and then use (-b/2a)

Question 19

how to go from standard to vertex form and vice versa

Answer 19

add a number to complete the square, then subtract it
factor the perfect square and solve the outer two numbers

from vertex to standard expand.

Question 20

how to go from standard to factored form and vice versa

Answer 20

Put all the terms on the left hand side, factor like a trinomal, or split up ax^2 and examine factors of c, then apply the zero product theorem to find vertex.

Question 21

how to find the parabola from a function

Answer 21

First, find the vertex, then the x intercepts, and then the y intercept. The graph accordingly.

Question 22

domain

Answer 22

The numbers included in x points (x = all real numbers)

Question 23

range

Answer 23

The numbers included in y points
(y > a)

Question 24

vertical line test

Answer 24

used to determine if the given graph represents a function: if the line intersects at at most one place its a function (no more than one intersection per vertical line)

Question 25

x intercepts from quadratic functions

Answer 25

vertex form = expand to standard form, then factor it to factored form.
Standard form = factor to factored form
Factored form = (p,0) (q,0)

Question 26

function

Answer 26

a set of ordered pairs in which the first corresponds to a distinct second coordinate. (no vertical points)