Based on the graph, determine is the discriminant is positive, negative or zero.

positive

Step-by-step explanation:

This graph at the vertex does not touch the x axis. So the answer is NOT going to be zero.

You have to go through the same procedure as the last question to be perfectly sure what the answer is.

Roots Form

The roots form  is one way to represent the quadratic. I would have used the vertex form but it is too hard to read the minimum. There is a lot of guessing.

y = a(x + 6)(x - 0.5)

Expand

y = a(x^2 + 6x - 0.5x - 3

y = a(x^2 + 5.5x - 3)                  

Remove the brackets

y = ax^2 + 5.5x*a - 3a

Use the y intercept to find a

y = - 2

x = 0

-2 = 0 + 0 - 3a

a = -2/-3

a = 2/3

Now represent the formula substituting 2/3 for a

y = 2/3 x^2 + 5.5(2/3) x - (2/3)*3

y = 2/3 x^2 + (11/3)x - 2

Now to the discriminate

D = sqrt(b^2 - 4*a*c)

a = 2/3

b = 11/3

c = - 2

D = sqrt( (11/3)^2 - 4(2/3)(-2) )

D = sqrt( 121/9 + 8*2/3)

D = sqrt(121/9 + 16/3)

D = sqrt(169/9)

Rule: Whether opening up or down if the vertex crosses the x axis then the discriminate will have a positive real value and must be evaluated to find the roots.        

answer: x= -2y

step-by-step explanation:

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1