Respuesta :
Answer:
x= 2 seconds
Step-by-step explanation:
Hello, I can help you with this
Step one
check the data
soccer ball was kicked in the air and follows the path h(x)=−2x2+1x+6
h(x)=−2x2+1x+6,using the correct format
[tex]h(x)= -2x^{2} +x+6[/tex]
where
x is the time in seconds
and
h is the height of the soccer ball
so, when the ball hit the ground its height is o (zero)
you need put this value into the equation and then isolate x to find its value.
Step two
find the value of x, when h=0
[tex]h(x)= -2x^{2} +x+6\\0=-2x^{2} +x+6\\using\\x=\frac{-b+\sqrt{ b^{2}-4ac }}{2a}\\ a=-2,b=1,c=6\\x=\frac{-1+\sqrt{ 1^{2}-4(-2)(6) }}{2*-2}\\x=\frac{-1+\sqrt{ 1^{2}+48}}{-4}\\x=\frac{-1+\sqrt{49}}{-4}\\x_{1} =\frac{-1+7}{-4}\\x_{2} =\frac{-1-7}{-4}\\x_{1} =-\frac{3}{2} \\x_{2} =\frac{-8}{-4} \\x_{2}=2[/tex]
we are looking for a time, so we only are going to use the positive x, it is X2
x= 2 sec
have a good day.
Answer:
At the time x = 2 seconds
Step-by-step explanation:
The height of the soccer ball is described by the function h(x), so if we want to know when the soccer ball will hit the ground, we just need to find the value of x that gives us the height zero, that is, h(x) = 0:
h(x) = −2*x^2 + 1*x + 6
0 = −2*x^2 + x + 6
2*x^2 - x - 6 = 0
Using Bhaskara's formula, we have:
Delta = b^2 - 4ac = 1 + 48 = 49
sqrt(Delta) = 7
x = (-b + sqrt(Delta)) / 2a = (1 + 7) / 4 = 2 seconds
