Question

A projectile is shot into the air following the path, h(x) = 3x 2 - 12x + 5. At what time, value of x, will it reach a maximum height?

A.) x = 1

B.) x = 2

C.) x = 4

D.) x = 5

Answer 1

The first thing you know is that this equation will most likely have an arch to it. To find the vertex, first put the equation in standard form which would be combining the common terms. So after a combination, you will have -9x +7 (I did not see a sign near your 2 on the second line) Then you can either graph it or plug in the numbers given.
A) -9 times 1= -9. -9+7= -2
B) -9 times 2= -18. -18+7=-11
As you continue your numbers will jut be decreasing so lets go with A

Answer 2

Option B. x = 2

Explanation:

A projectile is shot into the air following the path as h(x) = 3x² - 12x + 5

We have to find the value of x for which the height of the projectile is maximum.

Since projectile follows the path h(x) = 3x² - 12x + 5, a quadratic equation which means the path is in the form of a parabola.

Maximum height means vertex, which will be at the maximum height of the parabolic path.

Since x-coordinate of vertex of a parabola is represented by h =
`-(b)/(2a)`

From the given quadratic equation which is in the form of h(x) = ax² + bx + c

a = 3

b = -12

c = 5

Therefore, maximum height will be at x =
`(12)/(2*3)`

x = 2

Option B. x = 2 will be the answer.