vertex of parabola

Question

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

 

A. -5/3

B. 2

C. 3/10

D. -3/5

 

I keep coming up with 0. I know I have missed a step, please help.

Answer 1

 Without calculus, the  Horizontal Coordinate of a quadratic of  f(x) =aX^2 + bx + c  is equal to - b/ 2a

   Which in this case of

       f( X) =  - 5 X^2 + 3X + 2  

 

       equals :    - 3/[2(-5)] = -3/ -10 = 3/10 

Answer 2

Hi Christine;

f(x)=-5x²+3x+2

The vertex is the point at which the change of y is zero.  Therefore, we can take the first derivative of the function and calculate this...

0=-10x+3

-3=-10x

3/10=x

ANSWER C

Answer 3

If you have a graphing calculator you can visually see that the answer is C. 

There is a formula derived from the quadratic formula for the x coordinate of the vertex which is -b/(2a)  

For any parabola it will give you the x coordinate of the vertex. 

 

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

a=-5, b=3, c=2

 

-3/(2*-5) = 3/10

 

 

The answer is C. 3/10