Question

What is the range of the graph of \[y = –3(x – 4)^2 + 1\]

\[y\le 3\]

\[y\ge 3\]

\[y \le 1\]

\[y\ge 1\]

Answer 1

@Hero

Answer 2

Hint: Expand \((x-4)^2\)

Answer 3

(x-4)(x-4)...?

Answer 4

use the following for expansion
\[\Large (a-b)^=a^2+b^2-2ab\]

Answer 5

You forgot the squared symbol

Answer 6

\[x^2-8x+16\]

Answer 7

Now multiply that by 3 and add 1

Answer 8

\[-3x^2+24x-49\]

Answer 9

Now set

\(y = -3x^2 + 24x - 49\)

then use the vertex formula \(x = -\large\frac{b}{2a}\) to find the x value

Answer 10

After you find the x value, find the y value.

Answer 11

\[y=-1\]

Answer 12

Are you 100% sure about that?

Answer 13

I think you missed a sign when calculating

Answer 14

how do i know if its \[y\ge~or~~y\le\]

Answer 15

@Hero why not to make life easier and just put x=4 you will be left with 1 only ?

Answer 16

True

Answer 17

okay but how do i know which sign?? :\

Answer 18

Funny thing is, I keep getting y = -1

Answer 19

yes exactly O.O

Answer 20

yes that's good question.
multiply the whole equation with minus one (your orignal equation) always try to make the square term positive
always look for the sign of variable which is linear (in this case y)
so when you multiply with -1 the y will be negative
it means parabola will open towards -y axis

Answer 21

which means....??

Answer 22

put x=4 everything will be zero you will be left with 1 only.
this means
\[\Large y \le1\]

Answer 23

I see. He means to plug x = 4 back into the original equation to get y = 1

Answer 24

That let's you know that the y coordinate of the vertex is 1. The graph is concave down so the y values will go more negative and the graph progresses, which means that \(y\le1\)

Answer 25

here is helpful graph.
you can see here y will never be greater than 1
also parabola is open downward

Answer 26

Also, I just realized that your equation should have been

\(-3x^2 + 24x - 47\)

You added 1 rather than subtracted 1. That's why we kept getting y = -1

Answer 27

oh sorry