# Example 2 - Vertex Formula

##### [![image.png](https://library.naruzkurai.tk/uploads/images/gallery/2023-04/scaled-1680-/Qlw65k44qSbInUWl-image.png)](https://library.naruzkurai.tk/uploads/images/gallery/2023-04/Qlw65k44qSbInUWl-image.png)

##### a) y = 2x^2+4x 

1. 1. ##### we get the a, b, c in the formula <span style="text-decoration: underline;">y = ax^2 + bx + c</span>
        
        
        - ##### a = 2
        - ##### b = 4
        - ##### c = 0
    2. ##### then we plug in a, b into the formula
        
        
        - ##### x = -b / (2a)
        - ##### x = -4 / (2\*2) = -4/4 = -1

- ##### so the axis of symmetry is x = -1
- ##### to find the vertex
- ##### so the known vertex data is (-1, y)
- ##### to find y for the vertex we need to plug -1 into the formula y = 2x^2+4x
- ##### y = 2\*-1^2+4\*-1 = <span class="qv3Wpe" id="bkmrk--6">-6</span>
- ##### <span class="qv3Wpe">so the vertex is (-1, -6)</span>
    
    ##### <span class="qv3Wpe">-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=</span><span class="qv3Wpe">-=-=-=-=-=-=-=-=-=-=-=-=-=-=-</span>

##### B) y = -x^2 + 4x - 5   


1. 1. ##### we get the a, b, c in the formula <span style="text-decoration: underline;">y = ax^2 + bx + c</span>
        
        
        - ##### a = -1
        - ##### b = 4
        - ##### c = -5
    2. ##### then we plug in a, b into the formula
        
        
        - ##### x = -b / (2a)
        - ##### x = -4 / (2\*-1) = -4/-2 = <span class="qv3Wpe" id="bkmrk-2">2</span>

- ##### so the axis of symmetry is x = 2
- ##### to find the vertex
- ##### so the known vertex data is (2, y)
- ##### to find y for the vertex we need to plug -1 into the formula y = 2x^2+4x
- ##### y = -2^2 + 4 \* 2 - 5 = <span class="qv3Wpe" id="bkmrk--1">-1</span>
- ##### <span class="qv3Wpe">so the vertex is (2, <span class="qv3Wpe" id="bkmrk--1-1">-1</span>)</span>