Algebra MAC1105

Question

Without graphing, determine whether the quadratic function has a minimum or maximum value. What is the value ? F(x) = -2x²+ 8x +3

Answer 1

The negative sign in the quadratic term tells you it opens downward, so it has a maximum. There is more than one way to find the maximum. For example, you can find the vertex (h,k) by completing the square. The vertex is the maximum in this problem. You can also use the quadratic formula to find the x-intercepts. The x-coordinate of the maximum is the midway value between the x-intercepts. Evaluate F(x) at this midpoint to get the y-coordinate.

Answer 2

We define the following two conditions to find the max or min value:

If a>0, then there is a min point

If a<0, then there is a max point

Rewrite the equation:

f(x)=a*x^2+bx+c

Since a=-2, which is less than 0, then there is a max value.

To find the max value, the x value is defined by -b/2a. So,

x=-8/(2(-2))=2

y=f(x)=f(2)=-2*2^2+8*2+3=11

Therefore, the max point is at (2,11)

Have a good night! :)