what is the vertex of f(x)=-3x^2+7x+12

Question

I need to find the vertex and the x-intercepts

Answer 1

-b/2a is the formulas to find the vertex of a quadratic equation. You may always switch all of the signs of every term in an equation an so we can rewrite your function as 3x^2-7x-12. -b/2a will give us the x coordinate of the vertex. In this case -b is +7 and 2a is 2(3). Therefore 7/6 is the coordinate for the x value of the Vertex. 

Upon plugging in 7/6, we get: 3(7/6)^2-7(7/6)-12=3(49/36)-49/6-12=16.083333333...

vertex:(1.1666666...,16.0833333...)

 

Answer 2

To find the x-intercepts of a function set f(x) (or y) to zero. If you think about it graphically, the x-intercepts occur when your graph hits the x-axis, and the x-axis is the line y=0.

Now the equation looks like this: 0 = -3x²+7x+12

and you can use quadratic formula to find the x-values

x = [-7 +/- √(7²-4(-3)(12)) ] / [(2)(-3)]

x = [ -7 +/- √(49 +144) ] / -6

x = [-7 +/- √(193)] / -6

 

the vertex of your graph will fall in the middle of your x-intercepts, so if you take the average of your intercepts, that will be the x-value of your vertex, then you can plug that back into your function to solve for the y-value of the vertex