Question

What is the value of h when the function is converted to vertex form?

Note: Vertex form is p(x) = a(x − h)^2 + k .

p(x) = x^2 − 14x + 29

Enter your answer in the box.

h = ______

Answer 1

first we need to re-write the polynomial as a perfect square trinomial

take the b-coefficient (remember, the b coefficient is the number being multiplied to x), divide by 2, square the result, let me know what you get

Answer 2

The first term is, x2 its coefficient is 1 .
The middle term is, -14x its coefficient is -14 .
The last term, "the constant", is +29

Answer 3

AM I CORRECT ?

Answer 4

please follow my instructions

Answer 5

14x divided by 2

Answer 6

just the coefficient

-14, divide that by 2, then square it.

Answer 7

-7

Answer 8

after you divide it by 2, you must square it

what is (-7)^2 =?

Answer 9

49

Answer 10

good, so we add 49 to the polynomial

x^2 − 14x + 49 + 29

however, we must also subtract 49 from the end to keep the polynomial the same

x^2 − 14x + 49 + 29 - 49

now, we put this part in parentheses to make our trinomial

(x^2 − 14x + 49) + 29 - 49

Answer 11

now, factor this part:

(x^2 − 14x + 49)

Answer 12

(x - 7)^2

Answer 13

awesome, then we re-write the polynomial like so:

(x-7)^2 + 29 - 49

simplify the 29 - 49 part gives us

(x-7)^2 - 20

now, it's in vertex form

now let's put the two equations side by side

(x-h)^2 + k = (x-7)^2 - 20

what is the value of h?

Answer 14

14

Answer 15

let's just consider the exponential parts

put

(x-h)^2 and (x-7)^2 side by side

compare the two, what do you think h might be equal to?

Answer 16

h^2 - 2hx + x^2

Answer 17

if x - h = x - 7 what does h equal?

Answer 18

h = x - 7

Answer 19

x - h = x - 7

subtract x from both sides, what do you get?

Answer 20

h = 7

Answer 21

awesome so h = 7 = your answer

Answer 22

What are the x-intercepts of the quadratic function?

f(x) = x^2 − 3x − 10



Enter your answers in the boxes.


______ and ______

Answer 23

start by factoring it