Gallery of graphs

Question 1

what is the formula for a rectangular hyperbola

Answer 1

y = a/x-h + k

Question 2

what are the assymptotes of a rectangular hyperbola and truncus equivalent to?

Answer 2

x = h
y = k

Question 3

what is the domain (x) and range (y) when there are assymptotes for a graph?

Answer 3

domain of x is not equivalent to the x assymptote (greater than or less than the assymptote)
range of y is not equivalent to the y assymptote (greater than or less than the assymptote)

Question 4

what is the formula for a truncus graph?

Answer 4

y = a/(x-h)^2 + k

Question 5

what is the formula for square root graphs

Answer 5

y = a√ x - h + k

Question 6

how is the endpoint calculated?

Answer 6

(h,k)

Question 7

what is a equivalent to?

Answer 7

dialation

Question 8

what is h equivalent to?

Answer 8

horizontal translation

Question 9

what is k equivalent to?

Answer 9

vertical translation

Question 10

what is the shape of a rectangular hyperbola

Answer 10

Question 11

what is the shape of a truncus

Answer 11

Question 12

what is the shape of square root graph

Answer 12

Question 13

what is the shape of quadratic inequations graph

Answer 13

Question 14

define the steps of how to solve quadratic inequations

Answer 14

• rearrange so that the right hand side is zero
• sketch the graph of the left hand side solving y=0 to find the x-intercepts and paying attention to the concavity of the graph
• sketch the range of values of x which gives the correct range of the graph of the given inequality

Question 15

define how to determine the rules of a graph

Answer 15

using the information given (formula given), determine whether rectangular hyperbola, truncus, or square root graphs have to be used and sub in points to calculate

Question 16

recall the formula for the discriminant

Answer 16

∆ = b² - 4ac

Question 17

when ∆ > 0 there are…

Answer 17

2 solutions

Question 18

when ∆ = 0 there is…

Answer 18

one solution

Question 19

when ∆ < 0 there are….

Answer 19

no real solutions

Question 20

recall the three definitions of discriminant nature

Answer 20

• if ∆ is a perfect square and ∆≠0, there are two rational solutions
• if ∆ is not a perfect square and ∆>0, there are two irrational solutions
• if ∆= 0 there is one rational solution

Question 21

tangent meaning

Answer 21

intersecting once

Question 22

determine how to find the intersecting lines and parabolas

Answer 22

1. Make equations equal to each other
2. Rearrange to equal zero
3. Solve for x then substitute for y
4. Find the discriminant if required

Question 23

when given two x-intercepts by the question, determine the quadratic rule using..

Answer 23

factorised for: y = (x-b)(x-c)

Question 24

when given a turning point by the question, determine the quadratic rule using…

Answer 24

turning point formula: a (x-h)²+k

Question 25

when given three arbitary/ random points by the question, determine the quadratic rule using…

Answer 25

polonomial form: y = ax² + bx + c