2 years ago

Where do I put the points

Mathematics

1 answer:

Bezzdna [24]2 years ago

4 0

Answer:

Vertex : ( -1,-1)

Table : X Y

X Y

-3 3

-2 0

-1 -1

0 0

1 3

Plot the table that i just put on there and you should get the right answer.

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Eight students were asked how many books they read last summer. Their answers are listed below.

likoan [24]

Mode is 7 and the range is 6

6 0

3 years ago

Read 2 more answers

(X^4)-(45x^2)+324 what are the zeroes? And how many turning points?

dmitriy555 [2]

Zeroes:

We must solve

$x^4-45x^2+324=0$

To do so, we define the auxiliary variable $t=x^2$ . The equation becomes

$t^2-45t+324=0$

The quadratic formula yields the solutions

$t=9,\quad t=36$

Substituting back $t=x^2$ gives

$x^2=9 \iff x=\pm 3,\quad x^2=36 \iff x=\pm 6$

So, the zeroes are -6, -3, 3, 6.

Turning points:

Turning points are points where a function stops being increasing to become decreasing, or vice versa. Since functions are increasing when their first derivative is positive and decreasing when it's negative, turning points are points where the first derivative is zero.

We have

$f(x)=x^4-45x^2+324 \implies f'(x)=4x^3-90x$