In this week of foundations 11, i have learned the two other forms of quadratic equations, the vertex form and the factored form. I have learned how to take a vertex equation and be able to input a specific point the parabola goes through to be able to figure out the spacing is for the parabola.

You have the equation y=a(x-6)^2 + 3  and a point that the parabola goes through is (8,4). you would replace the 8 for where the x is and the 4 where the y is, to be able to find A. Once you do that, the equation would look like this… 4= a(8-6)^2 +3. you then do the brackets, 8-6. 4= a(2)^2+3. You then square the 2 in the bracket making it 4. the equation would then look like this… 4=4a+3. You would then subtract 3 from each side making the equation 1=4a. You then have to divide 4 from each side to isolate A. making it 1/4=A. The equation would then look like y=1/4(x-6)^2+3.

I could not upload a photo so i wrote it out.

Example: Finding A

Equation: y=a(x+7)^2 +6

Point that parabola crosses: (3,8)

Replace (3,8) with y and x in the equation

8=a(3+7)^2 +6

then you do the brackets

8=a(10)^2 +6

Then you square 10

8=100a+6

you then subtract 6 from each side

2=100a

then divide both sides by 100 to isolate A

leaving 1/50=A

then you replace A with the number you got from the original equation

y = 1/50 (x+7)^2 +6