From Standard to Vertex
How to do it?
For us to convert this standard form to vertex form, we are going to complete the square.
Here are the Steps!
1. Move the c value of the equation to the other side: -32+y = x^2 +12x
2. Now if you look at your right side, the b value is a 12. We must now add a number next to bx so that when we factor the right side, we will get a square. So lets add 36 since factoring the right side will give us (x+6)^2. Also if u add 36 to once side u must add it to the other. : -32+y+36 = x^2 + 12x + 36
3. Now we simplify! 4+y = (x+6)^2.
4. Now we bring 4 to the right side to isolate y : y = (x+6)^2 - 4
5. Now we have the vertex form!
How to use it?
Word Problem (Completing the Square)
a) What is the maximum height of the ball?
The maximum height of the ball is 1m.
b) At what horizontal distance does the ball reach its maximum height?
It reaches its maximum height at 4m.