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Answer:

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

There are zero x- intercepts of given function.

X- Intercepts:

To find x- intercepts, substitute [tex]y=0[/tex] in the function.

Given function is,  [tex]y=2x^{2} +5x+9[/tex]

Substitute [tex]y=0[/tex] in above equation.

              [tex]2x^{2} +5x+9=0\\\\[/tex]

The graph of function where crosses the x- axis that point is known as x- intercepts of function.

Graph of given function attached below, It is observed that graph will not crosses the x axis at any point.

Thus, There are zero x- intercepts of given function.

Learn more about the intercepts of function here:

https://brainly.com/question/26233

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