Question

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

Answer 1

Answer:

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

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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)

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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.