9. Consider the function: _3x² + 6x + 5
Find the vertex for the graph of the above equation and identify whether it 1 point
is a maximum or minimum. (Use Desmos)*
O (3,6). Maximum
O (-3, 6), Minimum
O (1,8): Maximum
O (1,8), Minimum

Answer : d. minimum (-1,3)

The vertex form of quadratic function is

, where (h,k) is the vertex

To get vertex form we apply completing the square method

To apply completing the square method , there should be only x^2

So we factor out 5 from from first two terms

Now we take the number before x (coefficient of x) and divide by 2

=1

Now square it

Add and subtract 1 inside the parenthesis

Now we take out -1 by multiplying 5

Now we factor x^2 +2x+1 as (x+1)(x+1)

h=-1  and k=3

So vertex is (-1,3)

When the value of 'a' is negative , then it is a maximum

When the value of 'a' is positive , then it is a minimum

is in the form of  

The value of a is 5

5 is positive so it is a minimum

f(x) is minimum at point (-1,3)

Step-by-step explanation:

b. 24 mm

step-by-step explanation:

use the pythagorean theorem.

a^2 + b^2 = c^2

a^2 + 7^2 = 25^2

a^2 + 49 = 625

a^2 = 576

a = 24

answer: b. 24 mm

option a.

step-by-step explanation:

if you look closely at the graph, we can notice that the function is not defined at two different points.

if you look at functions b and c, you will notice that both functions are not defined at just one point. the function b is not defined at x= -5/2 and function c is not defined at x=-5. both options are discarded, given that our function should not be defined at two fiferent points.

now, if you look closely at the graph you will notice that the function sketched is not defined at x=5 and x=-2.