what is the minimum y value on the graph of y=f(x) if f(x)=3x^2+3x-2

Answer 1

The minimum y value -2.75

y = f(x) = 3x² + 3x - 2

This is a parabola that opens upward so the minimum is its vertex.

The vertex can be found by using -b/2a to find the x coordinate then plug it in to find the y coordinate

a = 3

b = 3

c = -2

-b/2a = -3/2(3) = -3/6 = -1/2

-1/2 = the x coordinate of the vertex

y = 3(-1/2)² + 3(-1/2) - 2

y = 3(1/4) + 3/2 - 2

y = 3/4 - 3/2 -2

y = 3/4 - 6/4 - 8/4

y = (3 - 6 - 8)/4

y = -11/4 = -2.75

For a parabola that opens upward the vertex is typically the low point

You can graph your function at Desmos.com to comfirm this vertex and minimum

You can use the derivative to get the x coordinate then solve y to get the same coordinates of the minimum.