Question

If the y = ( x - 6)( x + 12) is graphed in the xy – plane, what is the x-coordinate of the parabola’s vertex?

Answer 1

Answer:

B) -3

Step-by-step explanation:

The zeros of the function are found easily from the factors. They are 6 and -12. The x-coordinate is halfway between them, at (6 + (-12))/2 = -6/2 = -3.

If you want a formula, consider a quadratic with roots (zeros) p and q. Then it factors as

... y = (x -p)(x -q)

The line of symmetry through the vertex is also the line of symmetry between the roots, so has x-coordinate:

... x = (p+q)/2

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In your problem, you have p=6, q=-12, so x = (p+q)/2 = -6/2 = -3 is the line of symmetry and the x-coordinate of the vertex.