Algebra 2: Chapter 5 Notes [DONE]

Question 1

what is the vertex form for graphing functions?

Answer 1

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

Question 2

what does h stand for? (3)

Answer 2

horizontal translations (left or right)

+ h = left
- h = right

Question 3

what does k stand for? (3)

Answer 3

vertical shifts (up or down)

up = + k
down = - k

Question 4

what does the sign a negative sign next to “a” stand for?

Answer 4

reflections across the x-axis

x-axis = negative (-)

Question 5

what does “a” stand for? (3)

Answer 5

a vertical stretch / compression by a factor of a.

if it’s bigger than 1, it stretches AWAY from the x-axis

if it’s smaller than 1, than it will compress towards the x-axis

Question 6

what does “b” stand for? (3)

Answer 6

a horizontal stretch / compression by a factor of 1/b

• if it is bigger than 1, it will stretch away from the y-axis
• if it is smaller than 1, it will compress towards the y-axis

Question 7

how do you find the axis of symmetry?

Answer 7

x = (-b) divided by 2a

Question 8

to find the vertex (h, k)?

Answer 8

plug x (axis of symmetry) into the function to find y.

Question 9

how to find the y-intercept?

Answer 9

the number w/o variables in the equation

ex. f(x) = x^2 - 4x + 6

6 = y-intercept

Question 10

how to know if the parabola opens upward or downward?

Answer 10

negative x^2 = downward

positive x^2 = upward

Question 11

how to determine if a parabola has a minimum or maximum value? (2)

Answer 11

upwards = minimum (all real numbers ≥ #)

downwards = maximum ( all real numbers ≤ #)

Question 12

minimum / maximum values can be found by…

Answer 12

doing x= -b divided by 2a, then plugging in x to the function. A.K.A. the vertex.

Question 13

how to find the zeros/roots of a function?

Answer 13

make the equation equal to 0

Question 14

general function to approximate the height in feet of a projectile on Earth after t seconds is…? (5)

Answer 14

h(t) = -16t^2 + v0t + h0

-16t^2 = the constant due to the Earth’s gravity

v0t = initial velocity

h0 = initial height

• the answer will have two solutions, the one that is negative is not possible, so therefore it will be the positive answer; ex. t = 0 or 5 –> only 5 seconds makes sense)

Question 15

finding zeros with a table ? (3)

Answer 15

1. find the vertex
2. make a table with 5 inputs and outputs, with the vertex in the middle
3. Graph.

Question 16

how to use zeros to write out a function?

Answer 16

ex.

x = 2 or x = -1

x-2 = 0 or x+1 = 0

(x-2) = 0 or (x+1) = 0

Question 17

how to find the numbers in terms of i?

Answer 17

1. factor out -1 from the square root
2. if its a perfect square, then multiply that by the number outside of the square root (if there is any)
3. the answer is #i

Question 18

quadratic formula?

Answer 18

x=(-b±√(b^2-4ac))/2a

Question 19

how to find the number of solutions using the discriminant?

Answer 19

b^2-4ac

Question 20

2 real solutions =

Answer 20

> 0

Question 21

1 real solution =

Answer 21

= 0

Question 22

2 complex (non real) solutions =

Answer 22

< 0

Question 23

what is the discriminant ?

Answer 23

c

Question 24

when do you complete the square, but subtract it on the other side?

Answer 24

when you’re writing the function in vertex form and identifying the vertex

Question 25

what does “-b” stand for?

Answer 25

it means that it will reflect across the y-axis