Select the x-coordinate of the vertex of the parabola defined in the function f(x)= -5x^2+3x+5?

answer choices are:
1. -5/3
2. 5
3. 3/10
4. -3/5

f (x) = - 5 [ x² - (3/ 5)x ] + 5

f (x) = - 5 [ x² - (3/5) x + 9/100 ] + 9/20 + 5

f (x) = - 5 [ x - (3/10) ]² + 109/20

x = 3/10 is x co-ordinate.

Re-write f(x) into vertex form which is y = a(x - h)^2 + k where (h, k) is vertex:

f(x) = -5x^2 + 3x + 5 = -5(x^2 - 3x/5 - 1)

= -5((x - 3/10)^2 - 109/100)

= -5(x - 3/10)^2 + 109/20

Therefore x coordinate of vertex is x = 3/10

Option 3

y = ax^2 + bx + c
x-coordinate of the vertex : -b/2a

a = -5, b = 3
x = -3 / 2(-5)
x = 3/10