Question

Which equation could generate the curve in the graph below?

Answer 1

d

Explanation:

Answer 2

`y=2x^2+8x+8`

Explanation:

Notice that we are looking for a quadratic function that has only one real solution for y=0, that is a unique point that touches the x-axis

We need therefore to look at the discriminant associated with all 4 equations constructed by equaling y to zero. We then try to find one that gives discriminant zero , corresponding to a unique real solution to the equation.

a)
`9x^2+6x+4=0` has discriminant:
`6^2-4(9)(4)=-108`

b)
`6x^2-12x-6=0` has discriminant:
`(-12)^2-4(6)(-6)=288`

c)
`3x^2+7x+5=0` has discriminant:
`(7)^2-4(3)(5)=-11`

d)
`2x^2+8x+8=0` has discriminant:
`(8)^2-4(2)(8)=0`

Therefore, the last function is the one that can have such graph