SOLUTION: 1. If y = a(x - 3)^2 + c and y = (2x - 3)(2x + b) represent the same quadratic function, find a, b, and c. (There are two possibles methods: i) expand both or ii) use the symmetry

Question 79946: 1. If y = a(x - 3)^2 + c and y = (2x - 3)(2x + b) represent the same quadratic function, find a, b, and c. (There are two possibles methods: i) expand both or ii) use the symmetry of the roots around the vertex.)
- I expanded both equations but I could not simplify the terms.
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Hello there,
Thank you in advance for your help. For the following problem, I was able to solve it using method 2, but I do not know how to solve it using method 1.
Best,
James
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!

Expand both equations:

Since these two equations represent the same quadratic function, the corresponding terms should be equal, so comparing term-for-term,...
First term:

Second term:

Substitute a = 4.

Third term:
Substitute a = 4 and b = -9

Check: Substitute a = 4, b = -9, and c = -9
First equation:

Second equation:

As you can see, the two equations are identical if:
a = 4, b = -9, and c = -9

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