SOLUTION: Pls help with this. Thanks. Factoring is an algebraic process, which is an essential one in the field of mathematics. Consider the following equation: y= x^2 + 2x - 8. This equatio

Algebra ->  Finance -> SOLUTION: Pls help with this. Thanks. Factoring is an algebraic process, which is an essential one in the field of mathematics. Consider the following equation: y= x^2 + 2x - 8. This equatio      Log On


   

Question 1183273: Pls help with this. Thanks. Factoring is an algebraic process, which is an essential one in the field of mathematics. Consider the following equation: y= x^2 + 2x - 8. This equation in factored form can be written as: y=(x-2)(x+4). Explain using words and algebra, how the zeros, the axis of symmetry, and the vertex can be obtained.
Found 3 solutions by Solver92311, MathTherapy, ikleyn:
Answer by Solver92311(821) About Me  (Show Source):
You can put this solution on YOUR website!


The two zeros can be found by setting each of the factors to zero and then solving for . Example: If one of the factors was , then the associated zero would be found by setting with the resulting zero being .

Once you have found the two zeros of a quadratic, the -coordinate of the vertex is exactly halfway between the two. For example, if the two zeros were and , then the -coordinate of the vertex would be .

The -coordinate of the vertex is simply the value of the function at the -coordinate you calculated as described above. Just substitute that value into the original equation (either the factored form or the unfactored form, you get the same answer either way given correct arithmetic) and do the indicated arithmetic.

John

My calculator said it, I believe it, that settles it

From
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Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Pls help with this. Thanks. Factoring is an algebraic process, which is an essential one in the field of mathematics. Consider the following equation: y= x^2 + 2x - 8. This equation in factored form can be written as: y=(x-2)(x+4). Explain using words and algebra, how the zeros, the axis of symmetry, and the vertex can be obtained. 
John (Solver92311) did a fantastic job explaining everything, and everything's correct. Tutor @IKLEYN is also correct. I was 

thinking about the distance from either of the x-coordinates (x , 0) to the axis of symmetry, and NOT the x-coordinate of the vertex.

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

x-coordinate of the vertex is   x%5Bv%5D = %28a%2Bb%29%2F2,  half of the way between the roots  "a"  and  "b".