What is the minimum and maximum value on the function y=5x^2+5x over the interval [0,3]?

Question

Only explain how to solve this problem in Algebra!

Answer 1

y = 5x² + 5x can be factored making it y = 5x(x + 1) so that the x-intercepts are x = 0 and x = -1 (to find the x-intercepts, set the y equal to zero and solve).

The vertex is halfway between the two x-intercepts so is at x = -1/2. The graph of the function opens up meaning the minimum value is at x = -1/2. The function increases on both side of the vertex.

So the minimum value on the interval [0, 3] will occur at the x-value closest to x = -1/2, which is x = 0. The minimum value is found by plugging in x = 0 so it is 5(0)² + 5(0) = 0.

And the maximum vale occurs at the x-value farthest away from x = -1/2 so x = 3. The maximum value is found by plugging in x = 3 so it is 5(3)² + 5(3) = 60.