Step-by-step explanation:
y = x^2 + 2x - 15
To find the x-intercepts, factor out the right side:
y = x^2 + 2x - 15
= (x + 5)(x - 3)
This means that the x-intercepts are at (-5, 0) and (3, 0).
Method 1:
The x-coordinate of the vertex of a parabola is given by the following:
x = -b/2a, where a = 1 and b = 2
= -(2/(2×1))
= -1
Using this value of x gives y = -16
Therefore, the coordinates of the vertex is (-1, -16).
Method 2:
We can find the x-coordinate of the vertex by taking the derivative of y and equating it to zero:
y' = 2x + 2 = 0 ---> x = -1
Using this value of x into our equation, we get y = -16.
Therefore,
vertex: (-1, -16)
