How many x-intercepts does the graph of y = 2x2 + 5x + 9 have?

The graph of y = 2x² + 5x + 9 has zero x-intercepts.

Step-by-step explanation:

x-intercepts are for y = 0.

Put y = 0 to the equation y = 2x² + 5x + 9:

2x² + 5x + 9 = 0

Calculate the discriminant of quadratic equation ax² + bx + c = 0:

Δ = b² - 4ac

if Δ < 0, then an equation has no solution

if Δ = 0, then an equation has one solution

if Δ > 0, then an equation has two solution.

2x² + 5x + 9 = 0

a = 2, b = 5, c = 9

Δ = 5² - 4 (2) (9) = 25 - 72 = - 47 < 0 - no solution