Find the x-intercept if the parábola with vertex (-1,-16) and y-intercept (0,-15)

x ∈ {-5, 3}

Step-by-step explanation:

The vertex form of the equation for a parabola with vertex (h, k) and vertical scale factor "a" is ...

... y = a(x -h)^2 +k

Your vertex and y-intercept allow us to find the value of "a" by putting these numbers into this equation.

... -15 = a(0 -(-1))^2 +(-16)

.. -15 = a -16 . . . . simplify

... 1 = a . . . . . . . . add 16

Then the vertex form of the equation of the parabola is ...

... y = (x+1)^2 -16

The x-intercepts occur where y = 0:

... 0 = (x +1)^2 -16

... 16 = (x +1)^2 . . . . . . . . . add 16

... ±√16 = ±4 = x +1 . . . . . take the square root

... -1 ±4 = x . . . . . . . . . . . . these are the x-intercepts: -5, +3

3

step-by-step explanation:

because where the point where the 2 lines intersect is (3,-1) the x value is 3