Question

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 1

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)

Explanation: