Find the x coordinate of the vertex....?

Question

y = (x - 5)(x + 3)


I think the answer is -4 or 8. But I may be wrong. Help is highly appreciated. :)

Answer 1

You need to convert the form of the equation of the parabola from the form to find the zeroes of the function to the vertex form. Do that by multiplying out the right side and completing the square.

y = (x - 5)(x + 3) = x² + 3x - 5x - 15
y = x² - 2x - 15
y + 1 = (x² - 2x + 1) - 15
y = (x - 1)² - 16

The vertex (h, k) = (1, -16).

The x coordinate of the vertex is 1.

Answer 2

So in a quadratic equation the x coordinate of the vertex can be given by the formula, -b / 2a, so if you mutiply that equation out you will end up y = x^2 - 2x - 15, so simply do, -b/2a, which is -(-2)/2(1), which is just equal to 1. So the vertex occurs when x =1. I dont know how you got -4 or 8. Glad to help. Email for any questions.

Answer 3

The general form of a quadratic equation is y = ax^2 + bx + c.
The formula for the x-coordinate of the vertex is -b/2a.
In order to get your equation into y= ax^2 + bx + c form, multiply it out using the foil method: First Outer Inner Last
y = (x - 5)(x + 3)
^ ^ first: x * x = x^2

y = (x - 5)(x + 3)
^ ^ outer: x * 3 = 3x

y = (x - 5)(x + 3)
^ ^ inner: -5 * x = -5x

y = (x - 5)(x + 3)
^ ^ last: -5 * 3 = -15

Now, add them all together. x^2 + 3x + (-5x) + (-15)
= x^2 - 2x - 15

To find the vertex, use -b/2a:
a= 1 b = -2

-(-2)/ [2 * 1] = 2/2 = 1

So, the x- coordinate of the vertex is 1.