What is the vertex of y=-3x^2+5x+6?

3 Answers
Jun 20, 2017

0.833, 8.083

Explanation:

The vertex can be found using differentiation, differentiating the equation and solving for 0 can determine where the x point of the vertex lies.

dy/dx (-3x^2 + 5x +6) = -6x + 5
-6x + 5 = 0, 6x = 5, x = 5/6

Thus the x coordinate of the vertex is 5/6
Now we can substitute x = 5/6 back into the original equation and solve for y.

y = -3(5/6)^2 + 5(5/6) + 6
y = 8.0833

Jun 20, 2017

(5/6,97/12)

Explanation:

"for a parabola in standard form " y=ax^2+bx+c

"the x-coordinate of the vertex is " x_(color(red)"vertex")=-b/(2a)

y=-3x^2+5x+6" is in standard form"

"with " a=-3,b=5,c=6

rArrx_(color(red)"vertex")=-5/(-6)=5/6

"substitute this value into the function for y-coordinate"

rArry_(color(red)"vertex")=-3(5/6)^2+5(5/6)+6=97/12

rArrcolor(magenta)"vertex "=(5/6,97/12)

Jun 20, 2017

(5/6,97/12)

Explanation:

y=ax^2+bx+c [Standard Form of a Quadratic Equation]
y=-3x^2+5x+6

a = -3
b = 5
c = 6

TO FIND THE X-VALUE OF THE VERTEX:
Use the formula for the axis of symmetry by substituting values for b and a:
x = (-b)/(2a)
x = (-5)/(2(-3))
x = (-5)/-6
x = 5/6

TO FIND THE Y-VALUE OF THE VERTEX:
Use the formula below by substituting values for a, b, and c:
y = (-b^2)/(4a)+c
y = (-(5)^2)/(4(-3))+6
y = (-25)/(-12)+6
y = 25/12+72/12
y = 97/12

Express as a coordinate.
(5/6,97/12)