Chap. 9 - Non linear relations and functions

Question 1

what is the basic form of a parabola?

Answer 1

y=x^2

Question 2

what is the turning point form of a parabola?

Answer 2

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

Question 3

what is the turning point derived from turning point form?

Answer 3

(h,k) ((x,y) respectively)

Question 4

what determines concavity and explain how the size of the number affects concavity.

Answer 4

a. if a is larger, the parabola is skinner, but if a is smaller, the parabola gets larger.

Question 5

when do you sketch via factorising?

Answer 5

when the parabola is in general form

Question 6

if the parabola is in general form, what key features can be derived without changing the equation?

Answer 6

*concavity (a)
*c is the y intercept

Question 7

how do you find x intercepts when the parabola is in general form

Answer 7

when y=0

Question 8

if the parabola is in general form, how do you find the x intercepts?

Answer 8

1. make y=0
2. factorise and those are the x intercepts

Question 9

the axis of symmetry is the average of:

Answer 9

the 2 x-intercepts

Question 10

to convert from general form to turning point form, use:

Answer 10

completing the square

Question 11

when a parabola is in general form, you can find the x intercepts in 2 ways. they are:

Answer 11

*completing the square, and then using turning point form
*the quadratic formula

Question 12

the axis of symmetry is equal to:

Answer 12

-b/2a

Question 13

the axis of symmetry is also:

Answer 13

the x coordinate of the turning point

Question 14

if you have the aos, you can find the TURNING point by

Answer 14

subbing the x-coordinate into the original equation.

Question 15

what makes a parabola negative definite?

Answer 15

if the parabola is concave down and always below the x axis.

Question 16

how do you determine if a parabola is negative definite?

Answer 16

if it has no x intercepts (use the discriminant)