How to Find the Vertex of a Quadratic Equation

Step-by-Step Guide

1. 1

   Step 1: Identify the values of a

   In this example, a = 1, b = 9, and c =
   18., The vertex is also the equation's axis of symmetry.
   
   The formula for finding the x-value of the vertex of a quadratic equation is x =
   -b/2a.
   
   Plug in the relevant values to find x.
   
   Substitute the values for a and b.
   
   Show your work: x=-b/2a x=-(9)/(2)(1) x=-9/2 , Now that you know the x-value, just plug it in to the original formula for the y value.
   
   You can think of the formula for finding the vertex of a quadratic function as being (x, y) = .
   
   This just means that to get the y value, you have to find the x value based on the formula and then plug it back into the equation.
   
   Here's how you do it: y = x2 + 9x + 18 y = (-9/2)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 , Now that you know that x =
   -9/2, and y =
   -9/4, just write them down as an ordered pair: (-9/2,
   -9/4).
   
   The vertex of this quadratic equation is (-9/2,
   -9/4).
   
   If you were to draw this parabola on a graph, this point would be the minimum of the parabola, because the x2 term is positive.
2. 2

   Step 2: and c. In a quadratic equation

3. 3

   Step 3: the x2 term = a

4. 4

   Step 4: the x term = b

5. 5

   Step 5: and the constant term (the term without a variable) = c. Let's say you're working with the following equation: y = x2 + 9x + 18.

6. 6

   Step 6: Use the vertex formula for finding the x-value of the vertex.

7. 7

   Step 7: Plug the x-value into the original equation to get the y-value.

8. 8

   Step 8: Write down the x and y values as an ordered pair.

Detailed Guide

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