Content

• To step
• Method 1 of 2: Method One: The formula x = -b / 2a
• Method 2 of 2: Method Two: Working out the equation
• Tips
• Warnings
• Necessities

The extreme value of a parabola is the maximum or minimum of the equation. If you want to find the extreme value of a quadratic equation, use a formula for it or solve the equation. Here you will learn how to do that.

To step

Method 1 of 2: Method One: The formula x = -b / 2a

1. Determine the values ​​of a, b and c. In a quadratic or quadratic equation holds X = a,X = b, and the constant (the term without a variable) = c. Suppose we are dealing with the following equation: y = x + 9x + 18. In this example, a = 1, b = 9 and c = 18.
2. Use a formula to find the value of x. The apex of the parabola is also the symmetry axis of the equation. The formula for finding the extreme value x of a quadratic equation is x = -b / 2a. Enter the relevant values ​​in this equation to X to find. Substitute the values ​​for a and b. Here's how:
   • x = -b / 2a
   • x = - (9) / (2) (1)
   • x = -9 / 2
3. Enter the value of x in the original equation to get the value of y. Now that you know x it is possible to apply this value to the original equation to get y. The formula for determining the extreme value of a quadratic equation is (x, y) = [(-b / 2a), f (-b / 2a)]. This just means that to get y, you can find x using this formula and then enter it into the original equation. Here's how to do that:
   • y = x + 9x + 18
   • y = (-9/2) + 9 (-9/2) +18
   • y = 81/4 -81/2 + 18
   • y = 81/4 -162/4 + 72/4
   • y = (81 - 162 + 72) / 4
   • y = -9/4
4. Write the values ​​for x and y as an ordered pair. Now that you know that x = -9/2, and y = -9/4, just write these values ​​as an ordered pair: (-9/2, -9/4). The extreme value of this quadratic equation is (-9/2, -9/4). If you would like to graph this parabola, this point is the minimum of the parabola, because x is positive.

Method 2 of 2: Method Two: Working out the equation

1. Write down the equation. Working out the equation is another way to find the extreme value of a quadratic equation. With this method it is possible to find the x and y coordinates immediately. Let's say we're working with the following quadratic equation: x + 4x + 1 = 0.
2. Divide each term by the coefficient of x. In this case, the coefficient of x is equal to 1, so you can skip this step. Dividing each term by 1 doesn't matter!
3. Move the constant to the right side of the equation. The constant is the term without a coefficient. In this case it is "1". Move the 1 to the other side of the equation by subtracting 1 from both sides. Here's how:
   • x + 4x + 1 = 0
   • x + 4x + 1 -1 = 0 - 1
   • x + 4x = - 1
4. Complete the square to the left of the equation. Work (b / 2) and add the result to both sides of the equation. Enter "4" as the value of bbecause "4x" is the b-term of the equation.
   • (4/2) = 2 = 4. Now add 4 to both sides of the equation to get the following:
     • x + 4x + 4 = -1 + 4
     • x + 4x + 4 = 3
5. Factor the left side of the equation. Now you will see that x + 4x + 4 is a perfect square. This can be rewritten as (x + 2) = 3
6. Use this to find the x and y coordinates. You can find the x coordinate by simply making (x + 2) equal to zero. So if (x + 2) = 0, what should x be? The variable x should then be equal to -2 to compensate for the +2, so the x coordinate is -2. The y coordinate is simply the constant term on the other side of the equation. So, y = 3. You can also take a shortcut and take the sign of the number in parentheses to find out the x coordinate. So, the extreme value of the equation x + 4x + 1 = (-2, 3)

Tips

• Understand what a, b and c represent.
• Show off and check your work! As a result, your teacher knows that you understand it and you yourself have the opportunity to see and correct errors in your elaborations.
• Stick to this sequence of editing to ensure a good outcome of the assignment.

Warnings

• Understand what a, b, and c represent - otherwise, the answer will be wrong.
• Don't worry - practice makes perfect.

Necessities

• Graph paper or computer
• Calculator