Question

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

Answer 1

ANSWER

See attachment.

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.