Question

Identify the vertex, the axis of symmetry, the maximum or minimum value, and the range of each parabola.

1.) Y=x^2+4x+1


Write each function in vertex form.

1.) Y=x^2+2x+5

A model for a company's revenue from selling a software package is R= -2.5p^2+500p, where p is the price in dollars of the software. What price will maximize revenue? Find the maximum revenue.

Answer 1

For a quadratic equation y=ax^2+bx+c, use x=-b/(2a) to find out the vertex
#1: a=1, b=4
x=(-4/2*1)=-2
Plug in x=-2 in the equation to find out the value of y: when x=-2, y=-3

so the vertex is at (-2, -3), the symmetry line is x=-2
the equation in vertex form is y=[x-(-2)^2]-3 =>y=(x+2)^2-3
Since the coefficient, a, of x^2, is 1 in this case, a positive number, the parabola opens upward, the equation has a minimum value, which happens at x=-2, and the minimum value is -3

use the same method for the other two questions