Question

Use the discriminant to determine which graph could represent the equation. y=x^2+4x+5

Answer 1

ANSWER

See attachment.

Step-by-step explanation

The given function is


`y = {x}^(2) + 4x + 5`

When we compare this function to


`y = a{x}^(2) + bx + c`

We have a=1, b=4 and c=5

We put this inside the formula for the discriminant, which is


`D = {b}^(2) - 4ac`


`D = {4}^(2) - 4(1)(5)`


`D = 16 - 20 = - 4`

Since the discriminant is negative, the function has no x-intercepts.

The graph of this function is the one hanging in the air above the x-axis and opens upwards.