quadratics functions polynomials

Question 1

How do you find the x-intercepts?

Answer 1

Plug y as zero

Question 2

How do you find the axis of symmetry?

Answer 2

The axis of symmetry is in between the x-intercepts.
Add the two x-intercepts and divide by two.
Can also be found by -b/2a

Question 3

How do you find the coordinates of the vertex?

Answer 3

Method One: use the axis of symmetry as a point for x and plug in for y

Question 4

a > 0

Answer 4

^_^ concave up

Question 5

the graph cuts the x-axis twice when

Answer 5

discriminant greater than zero

Question 6

the graph touches the x-axis if

Answer 6

discriminant is equal to zero

Question 7

the graph misses the x-axis when

Answer 7

discriminant is less than zero

Question 8

Definition of quadratic function

Answer 8

A quadratic function is a relationship between two variables x and y which can be written in the form
y=ax^2+bx+c
Where aa, bc, constants, a is not zero

Question 9

a < 0

Answer 9

concave down

Question 10

if -1 < a <1

a is not zero

Answer 10

the graph is wider than y = x^2

Question 11

if a < -1 or a > 1

Answer 11

the graph is narrower than

y = x^2

Question 12

general form

Answer 12

y = ax^2 + bx + c

Question 13

completed square form

Answer 13

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

Question 14

where is the vertex in completed square form?

Answer 14

h, k

Question 15

What is the discriminant

Answer 15

-b^2 - 4(ac)

Question 16

Positive definite quadratics

Answer 16

are quadratics which are positive for all values of x

ax^2 +bx +c > 0 for all x is Real number

Question 17

A quadratic is positive definite if and only if

Answer 17

a > 0

discriminant < 0

Question 18

Negative definite quadratics are

Answer 18

quadratics which are negative for all values of x.

ax^2 +bx +c < 0 for all x is Real number

Question 19

A quadratic is negative definite

Answer 19

a < 0

discriminant < 0

Question 20

factored form

Answer 20

f(x) = a(x-p)(x-q)

Question 21

what is p and q in factored form?

Answer 21

the x-intercepts

Question 22

If the line touches the curve, we can say that the line is __ to the curve.

Answer 22

If the line touches the curve, we can say that the line is tangent to the curve.

Question 23

The x-coordinates of any intersection points of the graphs can be found by solving the two equations __

Answer 23

simultaneously

Question 24

Tangent to the curve means

Answer 24

discriminant = 0

Question 25

Quadratic inequality

Answer 25

can be written in either the form ax^2 + bx + c >= 0
or
ax^2+bx+c where a is not equal to zero