select the x-coordinate of the vertex of the parabola defined by the function f(x)=-5x^2+9x+3

Question

select the x-coordinate of the vertex of the parabola defined by the function f(x)=-5x^2+9x+3.  Answers provided were

 

a.) -5/9

b.) 3

c.) 9/10

d.) -9/5

 

 

Answer 1

You need to write the equation in vertex form. 

f(x)=a(x-h)^2  + k. Then the vertex is at (h,k)

 

f(x)= -5x^2 + 9x + 3

     = -5(x^2 -9/5 x )+ 3    factor -5 out of x^2 and x terms

     = -5(x^2 -9/5 x + (9/10)^2) + 3 + 5(9/10)^2  Complete square

     = -5(x - 9/10)^2 +141/20

 

so h = 9/10

 

answer is c.

 

Answer 2

The x coordinate of the vertex is also the axis of symmetry. It is found using -b/2a

 

In the equation you are given, a =-5, b = 9 (these are the coefficients on the first and second terms.)

 

so the ratio would be -9/-10 or 9/10.