Optimal Value

The highest or lowest value that the graph reaches

In order to find the Optimal Value of a standard form equation, you must first find the Axis of Symmetry by following the formula -b . Last, you need to plug that value into the formula and then be
2(a) ax²+bx+c

For Example

To find the Optimal Value of the standard y=3x²+8x+10, you must:

Step 1: Make the B value negative (y=3x²+8x+10)

8 turns into -8

Step 2: Divide the negative b value and divide by 2(a) (y=3x²+8x+10)

-8

2(3)

Step 3: Solve

-8 -8

2(3) 6

The axis of symmetry is x= -1.33

Step 4: Now that you have the axis of symmetry, plug it into the original equation

y=3x²+8x+10

y=3(-1.33)²+8(-1.33)+10

y=5.3067-10.64+10

y=4.6667

Therfore, the Optimal Value is y=4.6667

Question

What is the Optimal Value of (y=2x²+10x+13)?

Solution

To find the Optimal Value of the standard y=2x²+10x+13, you must:

Step 1: Make the B value negative (y=2x²+10x+13)

10 turns into -10

Step 2: Divide the negative b value and divide by 2(a) (y=2x²+10x+13)

-10

2(2)

Step 3: Solve

-10 -10

2(2) 4

The axis of symmetry is x= -2.5

Step 4: Now that you have the axis of symmetry, plug it into the original equation

y=2x²+10x+13

y=2(-2.5)²+10(-2.5)+13

y=512.5-25+13

y=0.5

Therfore, the Optimal Value is y=0.5