## Learning Goals

1.) Change standard form to vertex form (completing the square)
2.) Find the vertex (maximum/minimum value)
3.) Use quadratic formula to find the x-intercepts
4.) Learn the importance of the discriminant
6.) Apply to word problems

## SUMMARY

COMPLETING THE SQUARE is when you change the first two terms of the standard form y=ax*+bx+c into a perfect square (vertex form) while maintaining the balance of original relation.

1.) Take coefficient of b (middle number) and divide it by 2 and square it.
2.) Then bracket the ax* and bx and find the common and take it out, which will be the a value.
3.) Put the number you get from square rooting in the equation and bracket it with the ax and b
4.) Make sure to do + and - of the number and leave the c out the bracket and solve

Eg. y=2x*+16x+3

y=2(x*+8x)+3
y=2(x*+8x+16-16)+3
y=2(x*+8x+16)-32+3
y=2(x*+8x+16)-29
Y=2(x+4)*-29

The vertex is (-4,-29)
The parabola is opening up so the minimum value will be (-29)

To solve this formula, you have to find a, b and c values from the standard form and plug them in the equation.

Eg. y=3x*+4x+7 a=3 b=4 c=7

DISCRIMINANT
-Is the (b*-4ac)/2a
-tells us if there's any possible solutions (x-intercepts)
-if discriminant is negative , there are no x-intercepts, the discriminant can't be squared
-if discriminant is 0, there will be one solution
-if discriminant is more than 0, there will be 2 solutions

2 solutions
1 solution
0 solution

## COMPLETING THE SQUARE EXAMPLE

❖ Completing the Square - Solving Quadratic Equations ❖