Answer to Question #279833 in Algebra for Nickle

Question

Given the quadratic relation y = x^2 + 2x - 15

Does the relation have a maximum or minimum value?

please show me how you got the answer and make sure it is right

Answer 1

y=x² +2x -15

Compare to the general equation of a quadratic equation: ax² +bx+ c

a=1, b= 2, c=-15

Since a is positive, it means the parabola (graph) opens upward and therefore will have a minimum value.

the x value of the vertex= -b/(2a)= -2/(2(1)) = -1

Substitute into the function

y= (-1)²+2(-1)-15

y= 1-2-15 =-16

Therefore, the minimum value of the parabola y=x²+2x-15 is -16. And the vertex is (-1,-16).