Question

If a quadratic equation is written in intercept form, y = (x-3)(x+5), then vertex is at...

Answer 1

The vertex is at (-1, -16).

Explanation:

We are given the quadratic equation:

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

And we want to find its vertex.

Recall that the x-coordinate of the vertex is also the axis of symmetry. Since a parabola is symmetric about the axis of symmetry, the axis of symmetry is halfway between the two roots.

From the equation, we can see that our two roots are x = 3 and x = -5.

Hence, the axis of symmetry or the x-coordinate of the vertex is:

`\displaystyle x = ((3) + (-5))/(2) = -1`

To find the y-coordinate of the vertex, evaluate the equation at x = -1:

`\displaystyle \begin{aligned} y(-1) &= ((-1)-3)((-1)+5)\\ &= (-4)(4) \\&= -16\end{aligned}`

Hence, the vertex is at (-1, -16).