Question

1. For what value(s) of k does the function f(x)=kx^2-8x+k have no zeros?
2. For what value(s) of m does g(x)=49x^2-28x+m have exactly one zero?

Answer 1

which one is giving you more trouble #1 or #2 ?

Answer 2

They're about the same level of difficulty for me

Answer 3

ok let's do #1 then

Answer 4

alright

Answer 5

notice how `kx^2-8x+k` matches up with `ax^2 + bx + c`

hopefully you see how
a = k
b = -8
c = k

agreed? or no?

Answer 6

yes

Answer 7

if you were to plug those three values into D = b^2 - 4ac, what would you get?

Answer 8

b^2-4ac=(-8)^2-4(k)(k)
=64-4k^2
square root of 64=8
" " of k^2=k

Answer 9

And i don't know what to do next

Answer 10

`1. For what value(s) of k does the function f(x)=kx^2-8x+k have no zeros? `\

for f(x) to have no real zeros, we need to force the discriminant D to be negative


D < 0
b^2 - 4ac < 0
64 - 4k^2 < 0


when is `64 - 4k^2 < 0` true? for what values of k?

Answer 11

what must i do to find the values of k?

Answer 12

one way is to graph y = -4x^2 + 64 using something like desmos

https://www.desmos.com/calculator

Answer 13

what are the x intercepts of y = -4x^2 + 64 ?

Answer 14

-4 and 4

Answer 15

which portions of the graph are below the x axis?

Answer 16

what do you mean by portions?

Answer 17

hopefully you see an upside down U shape?

Answer 18

oh yea i do!