Calculate the x values of the following quadratic functions y= 2x^2+11x+5?

To calculate the x values of the quadratic function y = 2x^2 + 11x + 5, we need to find the roots of the equation by setting y = 0 and solving for x.

0 = 2x^2 + 11x + 5

To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

In this case, a = 2, b = 11, and c = 5. Plugging these values into the formula, we get:

x = (-11 ± √(11^2 - 4*2*5)) / 2*2
x = (-11 ± √(121 - 40)) / 4
x = (-11 ± √81) / 4
x = (-11 ± 9) / 4

This gives us two possible values for x:

x1 = (-11 + 9) / 4 = -2 / 4 = -0.5
x2 = (-11 - 9) / 4 = -20 / 4 = -5

Therefore, the x values of the quadratic function y = 2x^2 + 11x + 5 are -0.5 and -5.

For a quadratic function in the form of y = ax^2 + bx + c, the x-values of the vertex (the turning point) can be found using the formula:

x = -b / 2a

In this case, a = 2 and b = 11, so the x-value of the vertex is:

x = -11 / (2 - 2) = -11 / 4

Therefore, the x-value of the quadratic function y = 2x^2 + 11x + 5 is -11 / 4.