Quadratic relations

Question

Given y = (x-3)(x+5) find the following 

 the x intercept as well as the coordinates 

the y intercept 

 the parabola max or min 

the max or min value 

 

Answer 1

To find the x-intercept, plug in y=0 and solve for x.

 

0 = (x - 3)(x + 5)

 

You will get two x values.  So you will have two x-intercepts.

 

 

To find the y-intercept, plug in x=0 and solve for y.

 

y = -3 * 5

 

y = -15

 

y-intercept is (0, -15).

 

 

To find the maximum or minimum, we expand the function.  Then we find the vertex.

 

y = x² + 2x - 15

 

 

Use the formula       h=-b/(2a)        to find the x-coordinate of the vertex.

 

where:

a = 1

b = 2

c = -15

 

h = -2 / (2 * 1)

h = -1

 

 

Evaluate y when x=-1.  This is the y-coordinate of the vertex.

 

y = (-1)² + 2(-1) - 15

y = 1 - 2 - 15

y = -16

 

The vertex is (-1, -16).  This is a minimum value, since we have a positive parabola.